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Multiscale modelling of snow depth over an agricultural field in a small
catchement in southern ontario, canada.
by
Robert Neilly
A thesis
presented to the University of Waterloo
in fulfillment of the
thesis requirement for the degree of
Master of Science
in
Geography
Waterloo, Ontario, Canada, 2011
© Robert Neilly 2011
ii
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including
any required final revisions, as accepted by my examiners.
I understand that my thesis may be made electronically available to the public.
iii
Abstract
Snow is a common overlying surface during winter-time and the redistribution of snow by wind
is a very important concept for any hydrological research project located within the cryosphere.
Wind redistributes snow by eroding it from areas of high wind speed, such as ridge tops and
windward slopes, and deposits it in areas of lower wind speeds, such as the lees of ridge tops,
vegetation stands, and topographic depressions. The accurate modelling of blowing snow
processes such as erosion, deposition, and sublimation have proven to be rather problematic. The
largest issue that many modellers must deal with is the accurate collection of solid precipitation
throughout the winter season. Without this, incorrect energy and mass balances can occur. This
thesis makes use of a new method of acquiring solid precipitation values through the use of an
SR50a ultrasonic snow depth sensor and then incorporates it into a version of the Cold Regions
Hydrological Model (CRHM) which includes the Prairie Blowing Snow Model (PBSM) and the
Minimal Snowmelt Model (MSM) modules. The model is used to simulate seasonal snow depth
over an agricultural field in southern Ontario, Canada and is driven with half-hourly locally
acquired meteorological data for 83 days during the 2008-2009 winter season. Semi-automated
snow surveys are conducted throughout the winter season and the collected in situ snow depth
values are compared to the simulated snow depth values at multiple scales. Two modelling
approaches are taken to temporally and spatially test model performance. A lumped approach
tests the model‟s ability to simulate snow depth from a small point scale and from a larger field
scale. A distributed approach separates the entire field site into three hydrological response units
(HRUs) and tests the model‟s ability to spatially discretize at the field scale. HRUs are
differentiated by varying vegetation heights throughout the field site. Temporal analysis
compares the simulated results to each day of snow survey and for the entire field season. Model
performance is statistically analyzed through the use of a Root Mean Square Difference
(RMSD), Nash-Sutcliffe coefficient (NS), and Model Bias (MB). Both the lumped and
distributed modelling approaches fail to simulate the early on-set of snow but once the snow-
holding capacities are reached within the field site the model does well to simulate the average
snow depth during the latter few days of snow survey as well as throughout the entire field
season. Several model limitations are present which prevent the model from incorporating the
scaling effects of topography, vegetation, and man-made objects as well as the effects from
certain energy fluxes. These limitations are discussed further.
iv
Acknowledgements
There are many people that I would like to thank that made it possible to complete this thesis.
First and foremost I would like to thank my advisor Dr. Richard Kelly who took a chance on me
and allowed me to come back to the University of Waterloo to join his excellent team of snow
scientists. His passion for the subject inspired me to want to learn as much as I could during my
tenure under his guidance. I especially want to thank him for allowing me the freedom to create
my own study. It may have been more time consuming and at times, painful but in the end it was
a great learning experience that I will never forget. Most importantly however, I would like to
thank him for his enduring patience from start to finish of this little project. First round‟s on me!
I‟d also like to thank Dr. Claude Duguay who provided me with the opportunity to gain some
valuable and memorable field experiences outside of my own study. I‟ll never forget our little
Alaskan snowmachine excursion in -65C weather. At Wilfrid Laurier University I would like to
thank Dr. Bill Quinton who introduced me to the Cold Regions Hydrological Model and helped
peak my interest in its applicability to modelling snow depth. I‟d also like to thank Dr. Mike
English, whose long-standing local connections at Strawberry Creek helped us establish contact
with the Zinger family who granted us permission to set up on Martz farm. At the University of
Saskatchewan I would like to thank Mr. Tom Brown and Mr. Matt Macdonald for their help and
support when I had a whole host of modelling questions. I feel as if it was a learning experience
for us all.
Secondly, but equally as important, I would like to thank my family for their support through this
entire process. They saw firsthand the process that I went through in order to complete this thesis
and they were there to listen to all the issues even when most of the time they didn‟t really
understand what I was talking about. They were also there for me during all „the other stuff‟ that
v
went on in my life and for that, I am very grateful. It was nice to know that I could always count
on them for support and to put a roof over my head or pay the odd bill when I needed it.
Lastly I would like to thank my friends and fellow students who graciously accepted the change
in topic whenever they would ask “are you done yet?”
vi
Table of Contents
AUTHOR’S DECLARATION ii
ABSTRACT iii
ACKNOWLEDGEMENTS iv
TABLE OF CONTENTS vi
LIST OF FIGURES ix
LIST OF TABLES x
LIST OF EQUATIONS xi
LIST OF SYMBOLS xiii
1. INTRODUCTION 1
1.1 THE NATURE OF SNOW IN THE WATER CYCLE 1
1.2 HYDROLOGICAL MODELLING 3
1.2.1 Small Scale Models 5
1.2.2 Regional Snow Models 5
1.2.3 Global Climate Models 6
1.2.4 Model Challenges 7
1.3 OBJECTIVES 9
1.4 THESIS LAYOUT 10
2. BACKGROUND 11
2.1 PHYSICAL PROCESSES OF SNOW 12
2.1.1 Precipitation 12
2.1.2 Density 13
2.1.3 Snow Depth 15
2.1.4 Snow Water Equivalent 15
2.2 ENERGY AND MASS BALANCE COMPONENT MODELS FOR A SNOWPACK 17
2.2.1 Energy Balance components 17
2.2.2 Shortwave Radiation Input (K) 18
2.2.3 Long-wave Radiation Input (L) 21
2.2.4 Sensible Heat Exchange with the Atmosphere (H) 22
2.2.5 Latent Heat Exchange with the Atmosphere (LE) 23
2.2.6 Heat Input from Rain (R) 23
2.2.7 Heat Input from the Ground 24
2.2.8 A comparison of Four Different Energy Balance Equations 24
2.2.9 Mass Balance Components 26
2.2.10 Sublimation, Evaporation, and Condensation of a Snowpack 27
2.2.11 Canopy Interception 27
2.2.12 Blowing Snow 28
2.3 BLOWING SNOW AND THE WINTER MOISTURE BUDGET 28
vii
2.3.1 The winter moisture budget 30
2.3.1.i Precipitation 30
2.3.1.ii Snow depth measurements 31
2.3.1.iii Sublimation 32
2.4 Summary of Energy Balance + Mass Balance of Snow 33
3. THE MODELS 35
3.1 THE PRAIRIE BLOWING SNOW MODEL 35
3.1.1 Saltation 35
3.1.2 Suspension 37
3.1.3 Sublimation 39
3.1.4 Erosion and Deposition 41
3.2 THE MINIMAL SNOWMELT MODEL 44
3.3 SUMMARY 45
4. METHODS 47
4.1 STUDY SITE 47
4.2 DIGITAL IMAGERY AND DATA 51
4.3 METEOROLOGICAL DATA 52
4.3.1 Ultrasonic snow depth sensors vs. traditional snow measurement techniques 53
4.3.2 Meteorological data alteration in order for proper model runs 56
4.4 SNOW SURVEYS 56
4.5 MODEL RUNS 58
4.5.1 Lumped Model – Point Scale 58
4.5.2 Lumped Model – Field Scale 59
4.5.3 Distributed Model – Field Scale 59
4.5.4 Model Parameters 59
4.6 MODEL TESTING AND VERIFICATION 64
4.7 SUMMARY 67
5. RESULTS 68
5.1 FIELD RESULTS 68
5.2 MODEL RESULTS 70
5.3 COMPARISON OF SIMULATED MODEL RESULTS AND OBSERVED
SNOW SURVEY RESULTS AT THE POINT AND FIELD SCALES. 72
5.3.1 Point Scale Results: Lumped 73
5.3.2 Field Scale Results: Lumped 74
5.3.3 Field Scale Results: Distributed 75
5.4 SUMMARY 76
6. DISCUSSION AND CONCLUSIONS 78
6.1 EVALUATING MODEL PERFORMANCE AND SOURCES OF ERROR 78
6.2 FUTURE CONSIDERATIONS 83
viii
6.3 CONCLUSIONS 84
REFERENCES 86
APPENDICES 94
APPENDIX 1 94
APPENDIX 2 96
ix
List of Figures
1-1 Classification of hydrological modelling by means of how they deal with the
factors of randomness, space, and time 4
1-2 SnowMIP2 analysis from Boulder, CO 7
2-1 A block of snow 17
2-2 Exponential decay of solar radiation with depth for a typical snowpack or glacier 20
2-3 Schematic diagram of the mass balance of a snowpack 26
3-1 Process of saltation and suspension of sediments into the atmosphere 36
3-2 Cross sectional view of a column of blowing snow 42
4-1 Location of Strawberry Creek field site 47
4-2 360 view of field sight from eight cardinal directions 49
4-3 Grand River watershed 50
4-4 In situ view of meteorological tower 53
4-5 Seasonal snow depth measurements from SR50a compared to manual snow depth
measurements from the Waterloo-Wellington International Airport 55
4-6 Map of snow depth transects 57
4-7 Distributed map of CRHM hydrological response units 60
4-8 Simplified schematic diagram of the progression of module observations through
the CRHM model modules 63
5-1 Corrected meteorological data from Strawberry Creek 69
5-2 Comparison of averaged model and observed snow depth 71
5-3 Comparison of averaged model and observed snow depth for each HRU in the
distributed modelling approach 72
x
List of Tables
1-1 Classification of snow 2
2-1 Classification scheme of SWE 16
4-1 List of selected meteorological instrumentation 52
4-2 CRHM model parameters 61
4-3 Characteristics of HRU parameters for blowing snow 62
5-1 Monthly climatic averages for Strawberry Creek (2008-2009 model season) and
Waterloo-Wellington International Airport (1971-2000) 68
5-2 Sample size of snow depth from each day of snow survey used for statistical
analysis 73
5-3 RMSD, NS, and MB results for the lumped modelling approach at the point scale 73
5-4 RMSD, NS, and MB results for the lumped modelling approach at the field scale 74
5-5 RMSD, NS, MB results for the distributed modelling approach at the field scale 75
xi
List of Equations
[2.1] Fresh snow density 1 14
[2.2] Fresh snow density 2 14
[2.3] Snow water equivalent (SWE) 15
[2.4] Simple equation to explain energy balance 17
[2.5] Net rate of energy exchange 18
[2.6] Net shortwave radiation 18
[2.7] Transmission, absorption, and reflectance of shortwave radiation 19
[2.8] Beer‟s Law 20
[2.9] Net longwave radiation 21
[2.10] Net longwave radiation under full cloud cover 22
[2.11] Sensible heat exchange with the atmosphere 22
[2.12] Sensible heat equation adapted for snow 22
[2.13] Latent heat exchange with the atmosphere 23
[2.14a] Heat input from the rain for a „wet‟ snowpack 23
[2.14b] Heat input from the rain for a „cold‟ snowpack 23
[2.15] Heat input from the ground 24
[2.16] Marsh‟s energy balance equation 24
[2.17] Male‟s energy balance equation 1 25
[2.18] Male‟s energy balance equation 2 25
[2.19] Net change in mass storage 26
[2.20] Snowfall canopy interception 27
[2.21] Maximum snowload on a canopy 28
[2.22] The winter moisture budget 30
[3.1] Saltation transportation 36
[3.2] Atmospheric friction velocity 36
[3.3] Roughness height for blowing snow 37
xii
[3.4] Suspension transportation rate 38
[3.5] Upper boundary height of a column of blowing snow 38
[3.6] Lower boundary height of a column of blowing snow 38
[3.7] Rate of change of mass with respect to time 39
[3.8] Nusselt and Sherwood Numbers 40
[3.9] Reynold‟s Number 40
[3.10] Ventilation velocity in the suspension layer 40
[3.11] Ventilation velocity in the saltation layer 40
[3.12] Undersaturation of water vapour with decreasing relative humidity with
increasing height 41
[3.13] Undersaturation of water vapour with increasing relative humidity with
increasing height 41
[3.14] Rate of sublimation 41
[3.15] Rate of erosion/deposition 42
[3.16] Mass balance equation for an HRU 43
[3.17] Sensible heat flux within the MSM module 44
[3.18] Latent heat flux within the MSM module 44
[3.19] Net radiation absorbed by snow surface within the MSM module 45
[3.20] Energy balance equation within the MSM module 45
[3.21] Mass balance equation within the MSM module 45
[4.1] Speed of sound in air 54
[4.2] Root mean square difference 65
[4.3] Nash-Sutcliffe coefficient 65
[4.4] Model bias 65
xiii
List of Symbols
Symbol Quantity SI Units
Roman capital letters
A surface area m3
Ast exposed silhouette area of a single vegetation element
CH surface exchange coefficient
Ch boundary layer coefficient m-0.27
s1.27
Csalt saltation constant m s-1
Cst coefficient for vegetation
Cz coefficient for prairie snowcover
D snow water equivalent depth mm
diffusivity of water m2s
-1
Dp Snow distribution factor
DH diffusivity of sensible heat m2s
-1
DM diffusivity of momentum in turbulent air m2s
-1
DWV diffusivity of water vapour in turbulent air m2s
-1
E evapotranspiration mm; kg m-2
s-1
EB blowing snow sublimation rate kg m-2
s-1
F downwind transport rate kg m-2
s-1
G heat input from the ground (substrate) W m-2
H sensible heat exchange with the atmosphere W m-2
I canopy interception kg m-2
I* maximum snow load kg m-2
I0 snow load kg m-2
K shortwave radiation input W m-2
K↓ incoming shortwave radiation W m-2
K↑ outgoing shortwave radiation W m-2
xiv
Ka Thermal conductivity of air W m-1
K-1
L* longwave radiation exchange W m
-2
L↓ incoming longwave radiation W m-2
L↑ outgoing longwave radiation W m-2
LAI leaf area index
LE latent heat exchange with the atmosphere W m-2
M molecular weight of water kg kmol-1
melt rate kg m-2
s-1
MB Model Bias
N total number of particles per unit volume
NS Nash-Sutcliffe coefficient
Nst number of vegetation elements per unit area m2
Nu Nusselt number
P air pressure; Pa
precipitation
snowfall rate kg m-2
s-1
Q* net all-wave energy W m-2
Q1 specific humidity at the measurement height
QG heat flux from the ground at the soil-snow interface W m-2
QH sensible heat flux W m-2
Qi energy flux due to net radiation, sensible and latent heat fluxes
and heat transfers from lower layers of the snowpack W m-2
QLE latent heat flux W m-2
QM available energy for melt W m-2
Qr radiant energy received by a particle W m-2
Qsat saturation humidity at the snow surface
Qsalt saltation transportation rate kg m-1
s-1
xv
Qsubl sublimation rate per unit area of snowcover kg m-2
s-1
Qsusp suspension transportation rate kg m-1
s-1
R heat input from rain W m-2
universal gas constant J kmol-1
K-1
Re Reynolds number
RMSD Root mean square deviation (same as obs/simulated)
Rs snowfall rate for a unit of time mm s-1
S net rate of energy exchanges; W m-2
Sublimation
SD snow depth m
Sh Sherwood number
Sp tree species coefficient
SWE snow water equivalent mm
Ta temperature of air K, (°C)
Tat absolute radiative temperature of the atmosphere and canopy °C
Tc cloud base temperature °C
Tr temperature of the rain °C
Ts surface temperature °C
Tss absolute temperature of the snow surface °C
Roman small letters
a extinction coefficient m-1
ca heat capacity of air at a constant temperature J kg-1
°C-1
ccan canopy coverage fraction
csubl sublimation loss rate coefficient
csuc snow unloading coefficient
cw heat capacity of water J kg-1
°C-1
xvi
dr particle size increment m
ds snow depth cm
dSWE/dt surface snow accumulation rate kg m-2
s-1
dT/dz temperature gradient of the soil
du/dt rate of change of internal energy KJ s-1
m-2
e base of Naperian logarithms
ei saturation vapour pressure over ice Pa
es vapour pressure at the surface Pa
g acceleration due to gravity m s-1
h specific enthalpy KJ kg-1
h* lower boundary of suspension layer
hs height of snow m
k von Karman’s constant m
kG thermal conductivity of the soil W m-1
°C-1
m measurement height m
mass kg
n sample size
n(z) mass concentration of suspended snow kg m-3
p precipitation mm
probability of blowing snow occurrence within the HRU
phi energy transfer due to precipitation kg m-2
s-1
qv vertical flux at the top of the controlled volume kg m-2
s-1
r rate of rainfall mm d-1
radius of snow particle contacting mass
u velocity of wind m s-1
u* atmospheric friction velocity m s-1
v kinematic viscosity of air m2 s
-1
xvii
vr ventilation velocity m s-1
ws terminal velocity m s-1
z vertical distance m
zb upper boundary of suspension layer
Greek capital letters
Δt change in time s
ΔQ change in heat energy absorbed by the snowpack W m-2
Δr net surface and subsurface horizontal exchange mm
ΔS net change in mass storage per unit volume kg; kg m-3
s-1
(per unit horizontal area) kg m-3
s-1
Ψ transmissivity
Greek small letters
α surface albedo
ε surface emissivity
εss emissivity of the snow surface
εat integrated emissivity of the atmosphere and canopy
ζ absorptivity
λf latent heat of fusion J kg-1
λs latent heat of sublimation J kg-1
λv latent heat of vapourization J kg-1
σ Stefan-Boltzmann constant W m-2
K-4
water vapour deficit with respect to ice
σ2 undersaturation of water vapour
ρa density of air kg m-3
ρs density of snow kg m-3
ρsat saturation density of water vapour kg m-3
ρw density of water kg m-3
xviii
Subscripts
a air
n sheer stress applied to non-erodible surfaces
o surface
observed values
s simulated results
t sheer stress applied to snow surfaces
1
Chapter 1.
Introduction
1.1 The Nature of Snow in the Water Cycle
Snow exerts a major influence on the environment and human activity on the Earth‟s surface.
Through its high albedo, it plays a significant role in the climate system and is a sensitive
indicator of climate change and variability. There are many locations in the world that are
seasonally covered with snow and people living in these locations have learned to adapt to its
many adverse and beneficial effects. Blowing snow on transportation, heavy snow loads on
structures and buildings, rapid snowmelt resulting in flooding (especially over frozen ground),
and acid-shock entering aquatic systems are just some of the examples of adverse effects of snow
(Hiemstra et al., 2002). Snow removal is a prominent feature in municipal budgeting and more
often than not, large snow storms can have a significant effect on a population‟s mobility due to
the disruption of power and transportation services. These same storms can also lead to an
increased amount of shovelling-related heart attacks, resulting in numerous cases of
hospitalization and even fatalities each year. Examples of beneficial effects include the fact that
snow acts as an insulator to flora and fauna, providing shelter from the harsh winter climates.
Melting snow augments soil water reserves and replenishes ground water supplies and reservoirs.
This is very important to agricultural activities in southern Ontario as many farms rely on the
melting of the seasonal snow cover to aid in ground water recharge, decreasing the need for
increased irrigation. Furthermore, the winter recreation industry relies heavily on seasonal snow
cover. In southern Ontario alone there are numerous downhill and cross-country ski centres, as
well as thousands of kilometres of groomed snowmobile trails for recreation.
2
Patterns of snow accumulation are not uniform across the globe. Its physical nature varies from
location to location and is highly dependent on latitude, altitude, and meteorological conditions
such as temperature, wind, relative humidity, and vapour pressure. Table 1-1 demonstrates a
simple classification of snow derived by Sturm et al. (1995) from an analysis of snow cover
meteorological conditions in Alaska.
Snow Cover Class Description
Tundra
A thin, cold, windblown snow. Maximum depth, ~75 cm. Usually found above
or north of tree line. Consists of a basal layer of depth hoar overlain by multiple
wind slabs. Surface zastrugi common. Melt features rare.
Taiga
A thin to moderately deep low-density cold snowcover. Maximum depth 120
cm. Found in cold climates in forests where wind, initial snow density, and
average winter air temperatures are all low. By late winter consists of 50-80%
depth hoar covered by low-density new snow.
Alpine
An intermediate to cold deep snowcover. Maximum depth, ~250 cm. Often
alternate thick and thin layers, common as well as occasional wind crusts. Most
new snowfalls are low density. Melt features occur but are generally
insignificant.
Maritime
A warm deep snowcover. Maximum depth can be in excess of 300 cm. Melt
features (ice layers, percolation columns) very common. Coarse-grained snow
due to wetting ubiquitous. Basal melting common.
Ephemeral
A thin, extremely warm snowcover. Ranges from 0 to 50 cm. Shortly after basal
melting common. Melt features common. Often consist of a single snowfall,
which melts away; then a new snowcover re-forms at the next snowfall.
Prairie A thin (except in drifts) moderately cold snowcover with substantial wind
drifting. Maximum depth, ~100 cm. Wind slabs and drifts common.
Mountain, special
cases
A highly variable snowcover, depending on solar radiation effects and local
wind patterns. Usually deeper than associated type of snowcover from adjacent
lowlands. Table 1-1. Classification of snow cover (Sturm et al., 1995)
Even though the different classes of snow cover were derived from data acquired in Alaska, they
are transferable to many locations. Southern Ontario experiences both ephemeral and prairie-like
snow covers depending on the time of year and climatological conditions. In terms of
hydrological modelling, the understanding of specific types of snow classes is important because
it can lead to appropriate parameterization in the modelled location.
3
This brief overview of snow highlights some of the environmental, economical, social, and
climatological aspects that snow has on our lives. Further information of the physical properties
of snow and its importance to energy and mass balance models can be found in Chapter 2.
1.2 Hydrological Modelling
Estimating snow accumulation from point in situ measurements and hydrologic models is an
important approach to help manage snow resources. To accurately predict or estimate a
hydrological process it is important to understand the nature of a system. A system is essentially
a set of equations linking the input and the output variables. These variables can be functions of
space, time, and whether or not there is an effect of randomness. Hydrological models are
“simplified models that are used to represent real-life systems and may be substitutes of the real
systems for certain purposes” (Diskin, 1970). To develop a model with time and space varying
parameter and variables is challenging. From a practical point of view it becomes necessary to
simplify the model by neglecting some of the sources of variation. Chow et al (1988) developed
a method of classifying hydrological models according to how they deal with these factors of
variation. This classification scheme (Figure 1-1) is created by asking three simple questions:
Will the model variables be random or not? Will they vary or be uniform in space? Will they
vary or be constant in time?
4
Figure 1-1: Classification of hydrological modelling by the means of how they deal with the factors of randomness, space,
and time. Modelled after Chow et al, 1988.
The first line in the classification scheme deals with how the model relates to the factor of
randomness. Although all hydrological phenomena often have some form of randomness, the
resulting variability in the model output may be quite small when compared to the variability
from known factors. When this is the case, a deterministic model is appropriate because this type
of model does not consider randomness. In a deterministic model, a given input always produces
the same output. Stochastic models on the other hand have outputs that are at least partially
random. When the random variation is large, a stochastic model is more appropriate due to the
fact that the actual output from such a model could be quite different from the output produced
by a deterministic model. This thesis uses a deterministic model, therefore, the following section
from this point forward deals solely with deterministic modelling rather than stochastic. For
more information concerning stochastic modelling, see Chow et al, (1988). It is important to note
that the above statements assume a normal distribution to the observed data. In some cases
however, a poor fit to observed data is obtained and a different distribution function should be
considered. As a hydrological example, if the probability of a certain number of events occurring
System
f (randomness, space, time)
Deterministic
Lumped
Steady FlowUnsteady
Flow
Distributed
Steady FlowUnsteady
Flow
Stochastic
Space-independent
Time-independent
Time-correlated
Space-correlated
Time-independent
Time-correlated
OutputInput
5
in a specified period of time is needed (e.g. when the temperature exceed a certain amount or
certain levels of snowfall are reached), then a Poisson and/or Gamma distribution are frequently
used.
The second line in the classification scheme deals with how the model relates to spatial variation.
Real life hydrological problems deal with space in all three dimensions but when it comes to
developing a model to practically represent such conditions, it can be quite cumbersome. A
deterministic lumped model spatially averages the system so that it is represented as a single
point in space without dimensions. Contrary to this, a deterministic distributed model defines the
model variables as functions of space by considering the hydrological process to be occurring at
various points in space.
The third line in the classification scheme deals with how the model relates to the variability of
time. Deterministic models can be broken down into either steady-flow models, where the flow
rate varies with time, and unsteady-flow.
Many hydrological models can provide the user with an accurate simulation over the required
domain. These models are generally quite simple and may in fact only be able to simulate a few
processes and tend to be rather small in scale. When attempting to increase the scale and/or the
number of processes being modelled, many hydrological models are coupled with land surface
models as well as atmospheric circulation models. These models range from being simple to
complex.
1.2.1 Small Scale Models
Most of the smaller scale snow models are one-dimensional energy balance models that deal
with a snow pack over a very small area. Some of the more complicated models venture into two
6
or three dimensions but are more susceptible to error due to an increase in the amount of
variables involved. Some examples of such models include: SNTHERM (Jordan, 1991),
SNOWPACK (Bartelt and Lehning, 2002), CROCUS (Brun et al., 1989), SnowTran-3D (Liston
and Strum, 1996) and the Prairie Blowing Snow Model (Pomeroy et al., 1993). These models are
straightforward although not always simple to use and require computing power. Input variables
for these models are primarily gathered from local meteorological stations.
1.2.2 Regional Snow Models
Larger scale models are designed to cover a larger area and can become more complicated as
they deal with regional scale processes. These types of models range from spatial models of
catchment run-off processes with strong snow showing (UEB (Tarboton et al., 1995)) to large-
scale land surface models (CLASS (Verseghy, 2000), MESH(Pietroniro, et al., 2006)). These
larger models will typically incorporate other small models within them which allow them to
simulate a number of processes, often simultaneously. In order to run these models successfully,
a larger number of forcing variables are necessary, due to the larger number of processes being
simulated, as well as a larger amount of computing power. Input variables for these models are
usually gathered from (but are not limited to) a network of local meteorological stations and
depending on the size of the study area, can also be remotely sensed from satellites and aircrafts.
1.2.3 Global Climate Models
The largest scalar models are lumped into the grouping of global climate models (GCM). These
models cover very large areas, require a large amount of input variables, and take time and
computing power to run. Examples of these models include the CGCM1 (Flato et al., 2000), the
ECHAM models (Roeckner, 1992, 1996, 2003, Roesch and Roeckner, 2006) and the HadCM3
(Gordon et al., 2000) to name a few. Due to the scale of these models, input variables are
gathered remotely through satellite sensors.
7
1.2.4 Model Challenges
The concept of scale is also very important as it determines the input requirements and the output
restrictions. Singh (1995) provides a brief outline into 25 different hydrological models. Of those
25 models, only 11 include snow processes (Singh, 1995). This demonstrates the problems that
many modellers face when attempting to design a model that can simulate the natural processes
that occur in the cryosphere during the snow accumulation and ablation season. In many cases,
the models do not consider every snow process and instead, focus on just a few. There is a
common belief that parameterization with accurate data and representative forcing data will
increase the model‟s accuracy. However, recent studies comparing many models clearly
demonstrate the inability of some models to accurately simulate the in situ conditions of snow
processes (Essery, et al., 2008, Rutter, et al., 2009). The SnowMIP (Model Inter-comparison
Project) was a comparison of atmospheric general circulation models, hydrologic snowmelt
models, numerical weather
prediction models, and detailed
avalanche and snow physics
models (Essery and Yang 2001).
Figure 1-2 demonstrates the
simulated results for snow water
equivalent (SWE) from the 24
models in the SnowMIP project.
The black lines are the model
runs from each model and the green
dots are the in situ measurements.
Figure 1-2: SnowMIP2 analysis from Boulder, CO. The solid black lines are
the model runs. The green dots are the in situ values. (from Rutter et al.,
2009)
8
This project is a clear example of how difficult it can be to simulate in situ observations and how
site-specific models can be. One of the main problems with snow modelling is the fact that each
model has been designed to simulate a specific type of landscape and may not (or on the rare
occasion, may) be transferable from one location to another without serious error.
This thesis is concerned with the application of the Prairie Blowing Snow Model (PBSM)
(Pomeroy et al., 1993). The model is a physically-based collection of algorithms that work in a
deterministic lumped fashion. Distributed models need to be altered and usually coupled with
other models in order to work properly. It was first develolped in 1987 as a single column mass
and energy balance that calculates blowing snow transport and sublimation rates (Pomerory,
1988,1989) and later extended to include a snow cover mass balance for the case of two
dimensions (Pomeroy et al., 1993). The model has been updated several times to deal with issues
including varying fetch and land use (Pomeroy et al., 1993) and varying terrain (Pomeroy et al.,
1997; Essery et al., 1999). The current version that is used in this thesis is based on the 1997
version and is a modified, single column calculation with updated methods to calculate the inputs
and scales of the fluxes from a point to a landscape in an areal snow mass balance calculation. It
is located as a module within the 6.0 platform of the Cold Regions Hydrological Model (CRHM)
(Pomeroy, 2007). CRHM is a modular modelling environment with a library of hyrological
modules which can be selected and linked together to simulate the hydrological cycle in the
natural environment. In this thesis, CRHM is used as a diagnostic tool to examine the blowing
snow processes and seasonal changes in the accummulated snowpack. CRHM separates the
landscape into individual units termed „hydrological response units‟ (HRUs). HRUs are the
largest landscape units having definable hydrological characteristics, meaning they can be
described by unique sets of parameters, variables, and fluxes (Pomeroy et al., 2007b). In order
9
for PBSM to work correctly it must be coupled to a snowmelt module. In this thesis it will be
coupled to the MSM (Minimal snowmelt model) model. Further details about PBSM and MSM
are found in the section devoted to the model descriptions.
1.3 Aims and Objectives
The aim of this thesis is to characterize snowpack changes throughout the 2008-2009 winter
season at Strawberry Creek, Ontario, and to consider the scaling effects of the model as it is
applied to various scales and in different formats with similar forcing data. To achieve this aim
three objectives are identified. The first of these objectives is to implement the PBSM and MSM
modules as a single model within the CRHM platform at the point scale. The second objective is
to implement the model over the entire agricultural field in a lumped format. The third objective
is to implement the model in a distributed format over the entire field.
a) Implementing PBSM and MSM at the point scale
The first objective is to implement the modules as a single model within the CRHM model
platform at the point scale and then assess the model performance at this scale. This scale is
defined as the area immediately surrounding the meteorological station (0.025km2).
b) Implementing the model over an agricultural field in a lumped format
The second objective is to scale up from the point scale and apply the model over the entire
agricultural field in a lumped format followed by assessing the model performance. This scale is
defined as the area contained within the property borders (0.406km2)
c) Implementing the model over an agricultural field in a distributed format
10
The third objective in this thesis is to implement the model at the same field scale as objective 2
but in a distributed format. The field is subdivided into three HRUs which have been determined
based on vegetation height. The model performance is then assessed to determine the effects of
vegetation height across the entire field at that scale.
1.4 Thesis Layout
This thesis is a modelling study of snow distribution in a blowing snow model by taking both a
lumped and distributed approach. Chapter 1 covers the basics of hydrological modelling,
problems associated with modelling snow, as well as a quick overview of snow properties.
Chapter 2 provides a more in depth look at the physical properties of snow as well as energy and
mass balance systems. Chapter 3 covers the background information about the models and
modules used in this thesis. Chapter 4 outlines the study site and methodology of the project at
Strawberry Creek. Chapter 5 displays the field results, both meteorological and snow survey, as
well as the model results. Model performance and statistical analysis are also covered in this
chapter. Chapter 6 further discusses the model performance as well as some of the sources of
error that affect the model performance. Future considerations and concluding remarks round out
this chapter.
11
Chapter 2.
Background – Snow accumulation and energy and mass exchanges through water
Seasonal snow falls and remains on the ground until later on in the season when it ablates. This
seasonal cycle of snowfall can be broken down into two phases; the accumulation phase and the
melting phase. The melt phase can be further broken down into phases of warming, ripening, and
output (Dingman, 2002).
The accumulation phase occurs when there is a general increase in water equivalent and a
decrease in temperature and net input of energy (Dingman, 2002). As snow falls through the
atmosphere it is subject to a variety of physical processes until it either becomes intercepted by
the vegetation canopy or is allowed to fall straight to the ground surface where it is further
subjected to physical and metamorphic processes over time. Once on the ground, these effecting
physical and metamorphic processes are dependent upon whether or not the snowpack is wet or
dry. A snowpack is considered „wet‟ when its temperature is at or above 0°C and a snowpack is
considered „cold‟ when its temperature is below 0°C. The accumulation phase is often dominated
by dry snow conditions. Under these conditions, the metamorphic processes depend on whether
the snowpack is isothermal or exhibits a temperature gradient (Male, 1980).
When the net energy within the snowpack is positive, the melt phase begins. The main processes
of melt are dependent upon climate and location. In temperate regions, radiation is the main
source of melt energy, followed by sensible and latent heat fluxes. Heat energy added by rain and
the ground can also play important roles during the melt phase in both temperate and arctic
environments.
12
The water which is generated from surface snow melt, or input from rainfall, results in a wet
snowpack. Wet snow causes different metamorphic processes then dry snow because it causes
smaller snow particles to disappear and allows larger particles to grow and fuse together with
other particles. This results in a snowpack with less structural strength between the particles and
a higher density. Colbeck (1978) states that the following loss in surface area causes a drop in
capillary potential and may be the reason that a pack can be observed to release a lot of water
very quickly in the early stages of melt.
Within the melt phase, the warming phase is the period in which the snow temperature increases
to 0°C, the ripening phase is the period at which the melting snowpack can no longer hold any
more water, and the output phase is the period when the snowpack releases the water (Dingman,
2002). The differentiation between all three of these melt phases is not always straightforward. A
snowpack can undergo several stages before reaching a stage of isothermal energy due to the fact
that there are large energy gradients between the atmosphere, snow, and ground which can cause
the snow within the pack to melt and refreeze several times throughout the season. In many
cases, snow will accumulate and melt several times in one season, often re-accumulating upon
partially melted snowpacks. This can complicate the prediction of net snow water equivalent.
The following section will discuss some of the physical properties of snow as well as the energy
and mass balances of a snowpack.
2.1 Physical Processes of Snow
2.1.1 Precipitation
Snow forms in the atmosphere where cloud temperatures are below 0°C. The large diversity of
initial snow shapes is a result of the variety of temperature and humidity conditions possible
13
during crystal formation. As the snow falls through the atmosphere, the changes in temperature
and humidity that the crystals encounter alters their form, compounded by collisions that further
modify their structure (Male 1980). Many factors affect the characteristics of snow from
formation to deposition. In the simplest of terms, precipitation can come in the form of rain or
snow, or as a mixture of rain and snow, depending on the meteorological conditions as
precipitation falls through the air. Further information on the various forms of precipitation,
specifically snow, can be found within The International Classification of Seasonal Snow on the
Ground (UNESCO/IHP, 2009).
2.1.2 Density
The density of snow is the mass per volume, usually specified in kilograms per cubic metre
(kg/m3). It is usually referred to as a ratio to the density of water (1000kg/m
3) and can vary
dramatically depending on temperature. The growth of individual snowflakes depends on
temperature and both the horizontal and vertical wind gradients. Predominately however, it is the
temperature that derives the overall size and shape of the snowflake (DeWalle and Rango, 2008).
Higher density snow usually results from warmer temperatures and/or higher winds whereas
lower density snow results from cooler temperatures and less wind. Warmer temperatures allow
snowflakes to rapidly decompose and coagulate with other snowflakes in the air or on the ground
surface. This increase in mass as well as the fact that the snowflake temperature is closer to the
melting point results in it having a higher density. Colder temperatures allow the snowflakes to
remain angular and faceted for a longer period of time in the air and on the ground surface. This
extended period of time results in a delayed coagulation of the snowflake with other flakes,
leading to lower density values. Higher wind speed can compact snow on the ground surface into
slab-like conditions, raising the density to a higher point then snow that has been left to settle at
14
lower wind speeds. New snow will have a much smaller density value then older snow due to
snow settling. This is because older snow within a snowpack has been exposed to periods of
melting, re-freezing, and wind fluctuations. As soon as a snowflake comes in contact with the
ground surface it begins to change shape, losing its angular, faceted structure and developing into
a small cluster of grains. Due to melting and re-freezing, these small grain clusters can coagulate
with other grain clusters within the snowpack, developing a hard packed surface with a high
density value. Fresh snow density has been found to vary from 70 to 100 kg/m3 by Goodison et
al. (1981). Male (1980,) reported that fresh snow density can vary from 10 to 500 kg/m3. La
Chapelle (1961) related snow density to air temperature from data collected at the Alta
Avalanche Study Center and derived an equation for calculating the density of fresh snow which
can be seen in equation 2.1. By examining the works of Diamond and Lowry (1953) and Schmidt
and Gluns (1991), Hedstrom and Pomeroy (1998) developed another equation for calculating the
density of fresh snow, which can be seen in equation 2.2 below.
[2.1]
[2.2]
In both equations, ρs (fresh) is the fresh snow density (kg/m3), and Ta is the air temperature (°C).
Snow density increases exponentially with time, as wind, sublimation, gravity, and warm periods
change the internal structure of the snowpack. The maximum density of a snowpack ultimately
depends on its location, landcover, and other factors (Fassnacht, 2000).
The snow density can also be measured using both in situ measurements as well as ground-based
remotely sensed measurements. In situ measurements are gathered through the use of snow pit
and gravimetric samples. Remotely sensed measurements include microwave radar (Frequency-
15
Modulated Continuous Waves and Ground Penetrating Radar) (Marshall et al., 2004), and
gamma ray attenuation.
2.1.3 Snow Depth
Snow depth is the accumulation of snow over a given period of time. The depth of snow at a
given area is a factor of the climatological conditions (temperature + precipitation), the
topography (slope + aspect), wind conditions (direction + velocity), as well as the land-use cover
and vegetation characteristics. Changes in snow depth can be the result of an increase in
accumulated precipitation after a snow storm, and can decrease due to melting. Furthermore,
snow depth varies in response to changes in snow density (e.g. decrease in volume without a
change to mass). For energy and mass balance purposes, it is more pertinent to measure a net
change in mass storage rather than just the depth of the snowpack. The snow cover depth can be
measured in situ or remotely sensed using an automated measuring device (e.g. MagnaProbe), a
snow ruler, graduated rod, aerial markers, and ultrasonic snow depth sensors (sonar).
2.1.4 Snow Water Equivalent
Snow water equivalent (SWE) is the equivalent depth of water of a snow covered area. Since a
uniform depth of 1mm of water spread over an area of 1m2 weighs 1kg, SWE is calculated from
the snow depth, ds, and the snow density, ρs, by the expression:
[2.3]
in which SWE is in mm when ds is in cm and ρs is in kg/m3 (Dingman, 2002). As the density of
the snowpack changes, so too will the SWE. An average density of 100kg/m3 is often assumed
for freshly fallen snow. This gives 1 unit of water equivalent for 10 units of snow depth. It is
16
however, not appropriate to use a common conversion for all environments (Pomeroy and Gray,
1995). Once the amount of water equivalent is established, it becomes simple to determine how
much energy is needed to either melt or freeze this depth of water given the appropriate latent
heat values.
Term Remarks
Approximate
Range of θ
Graphic
Symbol
Dry
Usually T is below 0°C, but dry snow can occur at any
temperature up to 0°C. Dissaggregated snow grains have little
tendency to adhere to each other when pressed together, as in
making a snowball
0%
Moist T = 0°C. The water is not visible even at 10 x magnification.
When lightly crushed, the snow has a distinct tendency to
stick together.
<3%
Wet
T = 0°C. The water can be recognized at 10 x magnification
by its meniscus between adjacent snow grains, but water
cannot be pressed out by moderately squeezing the snow in
the hands. (Pendular regime)
3-8%
Very Wet
T = 0°C. The water can be pressed out by moderately
squeezing the snow in the hands, but there is an appreciable
amount of air confined within the pores. (Funicular regime)
8-15%
Slush T = 0°C. The snow is flooded with water and contains a
relatively small amount of air. >15%
Table 2-1. Classification scheme of SWE (Colbeck et al, 1990)
Table 2-1 shows that there are many different classification terminologies that can be assigned to
a certain percentage of liquid water content (θ). Much like the depth and density, the SWE can be
measured both in situ as well as by using a variety of remote sensors. In situ measurements
include gravimetric sampling and snow pillows. Remotely sensed measurements (satellites,
aircraft, etc) make use of algorithms and values of snow depth and density.
17
2.2 Energy and Mass Balance Component Models for a Snowpack
The following section provides a basic theoretical background for many different mathematical
components that pertain to snow processes. It is important to have this background knowledge in
order to fully understand how the model arrives at its results as well as to better understand what
is naturally occurring in the environment.
2.2.1 Energy Balance components:
There are many different energy balance models that exist for snow but the differences between
these models are quite subtle. In order to completely understand the mathematical models
pertaining to snow it is necessary to view the snow in a finite condition. Figure 2-1 demonstrates
a typical block of snow and describes the energy balance associated with that element of snow of
surface area A and height hs.
Figure 2-1: A Block of Snow (Dingman, 2002)
Dingman (2002) provides a simple equation to explain this energy balance and can be seen
below:
[2.4]
18
Where S (E L-2
T-1
) is the net rate of energy exchanges into the element by all processes over a
time period Δt (T), and ΔQ (E L-2
) is the change in heat energy absorbed by the snowpack during
Δt. Dingman expresses the measurable quantities of S, Δt, and ΔQ in terms of fundamental
physical dimensions of energy [E], length [L], and time [T]. The net rate of energy exchange, S
(W m-2
) can be expanded, as seen in Equation 2.5:
[2.5]
Where K (W m-2
) is the shortwave radiation input, L (W m-2
) is the long-wave radiation input, H
(W m-2
) is the sensible heat exchange with the atmosphere, LE (W m-2
) is the latent heat
exchange with the atmosphere, R (W m-2
) is the heat input from rain, and G (W m-2
) is the heat
input from the ground. Determining a complete energy balance for a given snowpack is
complicated. As will be discussed below, each term in Equation 2.5 can in turn be difficult to
acquire due to the constant fluctuation of shortwave radiation penetration depths and diurnal and
seasonal thermal variations within the snowpack.
2.2.2 Shortwave Radiation Input (K):
The net shortwave radiation input is described in Equation 2.6.
[2.6]
K↓ is the incoming shortwave radiation, K↑ is the outgoing shortwave radiation, and α is the
albedo. Albedo is the representation of the fraction of radiation reflected from the snow surface
and can vary from 0.04- 0.95, with new snow having the highest values and lesser values as the
snow ages (Oke, 1987). Since snow is highly reflective, even the shallowest of snow covers
alters the land surface albedo. Furthermore, the albedo of snow can vary diurnally with higher
19
values occurring in the early morning and later in the evening when solar incidence angles are
low. At these lower angles, specular reflection dominates over diffuse reflection. Meteorological
conditions such as cloud cover, seasonality, and the physical state of the snowpack can all have
an influence on the albedo as well, allowing even more diurnal variation. The albedo for snow
also varies with wavelength where higher albedo is found with shorter wavelengths and lower
albedo with longer wavelengths.
Snow differs from other surfaces because it allows some transmission of shortwave radiation
throughout the snowpack. This means that at any depth, the shortwave radiation can be
transmitted (Ψ), reflected (α), or absorbed (ζ) according to the following equation (Oke, 1987):
[2.7]
It is interesting to note however, that this transmittance, absorption, or reflectance of shortwave
radiation is not universal throughout the vertical profile of the snowpack. The shortwave
radiation at the surface (K↓0) is much stronger than that found at any depth below. As the
shortwave radiation passes through the upper layers of the snow profile it begins to lose intensity
at an exponential rate.
20
Figure 2-2: Exponential decay of solar radiation with depth for a typical snowpack and glacier. (Oke, 1987 after Geiger,
1965)
According to Beer’s Law:
[2.8]
the shortwave radiation reaching any depth z, is dependent on the shortwave radiation K↓z at
depth z, the base of natural logarithms e, and an extinction coefficient a (m-1
). The extinction
coefficient is dependent on the nature of the medium that is being transmitted through and the
wavelength of the radiation. As can be seen in the above diagram (Figure 2-2), snow has a larger
coefficient than ice, therefore snow has a much shallower penetration depth. This penetration
depth can be as great as 1m for snow and as much as 10m for ice (Oke, 1987).
The transmission of solar radiation within a snowpack can create problems when trying to
monitor or observe the radiation for energy balance purposes. Instruments mounted above the
snow surface may not only be measuring the reflectance from the surface but also some of the
reflectance from some of the subsurface layers. The resulting albedo calculation would therefore
be a volume and not a surface value.
21
2.2.3 Long-wave Radiation Exchange (L*):
The net long-wave radiation exchange is described in Equation 2.9.
[2.9]
L↓ is the incoming long-wave radiation, L↑ is the outgoing long-wave radiation, εss is emissivity
of the snow surface, εat is the integrated effective emissivity of the atmosphere and canopy, and σ
is the Stefan-Boltzman constant (5.67 x 10-8
W m-2
K-4
). Tat is the absolute radiative temperature
of the atmosphere and canopy and Tss is the absolute temperature of the snow surface. Snow
(especially fresh snow) is almost a perfect radiator. The emissivity of snow is usually assumed to
be 1.0 but much like albedo, it too can vary with the age of the snow from 0.85 – 0.99 (Oke,
1987) as well as due to metamorphological processes (Grody, 1996). Even though the emissivity
can be relatively high, the surface temperature Tss is low, leading to L↑ being overall, quite small.
One of the major issues with implementing Equation 2.9 can be found in properly estimating
absolute values for εat and Tat, or equivalently, to estimate a value for L↓ under various
conditions of cloudiness and forest cover. Methods for estimating L↓ can be found in Dingman
(2002).
Oke (1987) presents a very interesting scenario for estimating L↑ when the snow surface is
melting (T0 = 0°C [273.2 K]). If we assume ε for snow to be a value of 1, and the surface
temperature to be at the freezing point, then the value of L↑ is constant at 316 W m-2
(substituting into equation 2.9). If this melting occurs under complete cloud cover, then the net
long-wave exchange (L*) between a fresh snowpack and the overcast sky becomes a function of
their respective temperatures due to the fact that clouds are also close to being full radiators. This
process can be seen in the following equation:
22
[2.10]
where Tc4 is the cloud base temperature. If the cloud base temperature is warmer then the snow
surface temperature then L* will be positive. Under clear skies however, L
* is almost always
negative.
2.2.4 Sensible Heat Exchange with the Atmosphere (H):
When vertical temperature gradients and turbulent eddies exist above the surface, sensible heat is
transferred to the atmosphere. Equation 2.11 expresses the sensible heat exchange with the
atmosphere.
[2.11]
DH is the diffusivity of sensible heat, DM is the diffusivity of momentum in turbulent air, ca is the
heat capacity of air at a constant temperature (J kg-1
°C -1
), ρa is the density of air (kg m-3
), k is a
dimensionless constant (0.4), um is the velocity of wind (m s-1
) at height zm (m), zd is the zero-
plane displacement, z0 is the roughness height (m), Ts is the surface temperature (°C), and Tm is
the temperature of the measurement height (°C). This equation can further be adapted for snow if
we assume that both the wind speed, vm, and air temperature, Ta, are measured at the same
height, zm (typically 2m above the ground surface), that the diffusivity of sensible heat and
momentum are the same (DH =DM), and finally, that the zero-plane displacement, zd, is
negligibly small. With these assumptions Equation 2.11 becomes
[2.12]
23
2.2.5 Latent Heat Exchange with the Atmosphere (LE):
When turbulent eddies and a vertical pressure gradient are both present, latent heat (water
vapour) is transferred to the atmosphere. Equation 2.13 expresses the latent heat exchange with
the atmosphere.
[2.13]
In addition to the terms that have already been defined above, DWV is the diffusivity of water
vapour in turbulent air, λv is the latent heat of vaporization (J kg-1
), P is the air pressure (mb), es
is the vapour pressure (Pa) at the surface and em is the vapour pressure (Pa) at height zm.
2.2.6 Heat Input from Rain (R):
There are two equations that apply to the heat input from rain. These two equations are
dependent on whether or not the snowpack is a „wet‟ snowpack at or above the freezing point
(Equation 2.14a) or if the snowpack is a „cold‟ snowpack below freezing (Equation 2.14b).
[2.14a]
[2.14b]
ρw is the density of water (kg m-3
), cw is the heat capacity of water (J kg-1
°C -1
), r is the rate of
rainfall (m s-1
), and Tr is the temperature of the rain (°C). The only additional term for the heat
input from rain in a snowpack below freezing is λf, which is the latent heat of fusion. If rain
percolates through the snowpack it becomes an additional heat source which can then melt the
surrounding snow and/or result in a possible addition to meltwater run-off.
24
2.2.7 Heat Input from the Ground (G)
Summer storage of thermal energy results in temperatures in the soil profile to increase
downwards from the snowpack. The rate of heat that is conducted to the base of this snowpack is
described in Equation 2.15.
[2.15]
kG is the thermal conductivity of the soil (W m-1
°C-1
) and dT/dz is the vertical temperature
gradient in the soil. G becomes significant when the snowcover over top of the ground surface is
thin and there a heat exchange across the base of the snowpack (Oke, 1987). When the snowpack
is larger, it acts as a thermal insulator and the effect of G becomes rather unimportant (Oke and
Hannell, 1966). Dingman (2002) states that G is usually negligible during a snowmelt season,
but can be significant during the accumulation season.
2.2.8 A comparison of Four Different Energy Balance Equations:
The following section will examine several energy balance equations as they pertain to varying
types of snowpack and how they deal with the different types of energy. For a more in depth
comparison of snowmelt energy balances see Kuusisto (1986). The first of the four equations
was put forth by Dingman (2002) and described above as Equation 2.5. The second equation
comes from Marsh (1990) and is described below as Equation 2.16.
[2.16]
QM (W m-2
)is the available energy for melt (latent heat storage due to melting or freezing), Q*
(W m-2
) is the net all-wave radiation (K + L), QH (W m
-2) is the sensible heat flux, QE is the latent
25
heat flux, QR (W m-2
) is the heat flux from rain, QG (W m-2
)is the heat flux from the ground at
the soil-snow interface, and dU/dt (KJ s-1
m-2
) is the rate of change of internal energy. The third
and fourth equations both come from Male (1980) and can be seen as Equations 2.17 and 2.18
respectively below.
[2.17]
[2.18]
In Equation 2.17, Qi (W m-2
) is the energy flux due to net radiation, sensible and latent heat
fluxes, and heat transfer from the lower layers of the snowpack. (ph)i is the energy transfer due to
precipitation, p (kg m-2
s-1
) with an associated specific enthalpy, h (KJ kg-1
). The second of
Male‟s equations, Equation 2.18, dU/dt (KJ s-1
m-2
) is the change in internal energy of the pack.
Male (1980, p.349) states that Equation 2.17 only requires measurements taken at or near the
upper surface and is therefore suitable for deeper snowpacks. Equation 2.18 describes the entire
thermal regime of the snowpack and can be practically used for shallow snowpacks of less than
40cm. When horizontal advection is substantial (i.e. not near open water, or patchy snow cover),
neither equation is considered valid.
Of all the equations presented above, Equation 2.17 is the simplest. Equations from Dingman
(Equation 2.5), Marsh (Equation 2.16), and Male (Equation 2.18) all consider the internal energy
of the snowpack but the latter two equations also include the melt energy. In Equation 2.16 the
melt energy remains in the form of energy but in Equation 2.18, the melt energy is actually the
melt-water from the bottom of the snowpack. Both of Male‟s equations focus primarily on the
melt phase but, as was previously mentioned, could be used for the accumulation phase so long
as the conditions of negligible horizontal advection are met. Dingman and Marsh‟s equations
26
include both the accumulation and melt phases and are assumed to work for a snowpack of any
depth. For the sake of this thesis the above statements shall remain strictly theoretical but a quick
application of a common data set would help to better understand the differences among and uses
between each equation.
2.2.9 Mass Balance Components
Acquiring a proper mass balance for a given snowpack can be rather difficult due to the constant
phase changes occurring within the snowpack throughout the season. As was discussed in the
above sections, a snowpack can be influenced by a variety of different factors that can result in
diurnal and seasonal fluctuations in both the energy and mass balances.
Figure 2-3: Schematic diagram of the mass balance of a snowpack (after Oke, 1987)
A simple mass balance can be determined if we assume a snowpack where the top section is
exposed to the air interface and its lower section is either at the ground interface or is at a depth
of negligible water percolation (Figure 2-3), we can assume that the net change in mass storage
ΔS, is given by:
[2.19]
27
Where p is the precipitation input from either snow or rain, E is the net turbulent exchange with
the atmosphere and can be in the form of condensation, sublimation (inputs) or evaporation and
sublimation (outputs), and Δr the net surface and subsurface horizontal exchange (surface snow
drifting and meltwater flow or subsurface meltwater throughflow) (Oke, 1987).
2.2.10 Sublimation, Evaporation, and Condensation of a Snowpack
As was mentioned above, water within a snowpack is susceptible to the physical processes of
sublimation, evaporation, and condensation. These processes are driven by the vapour pressure
gradient between the surface of the snowpack and the atmosphere. When the vapour pressure
above the snowpack is greater than the vapour pressure at the surface, condensation occurs.
When the vapour pressure above the surface is lower than the vapour pressure at the surface,
sublimation or evaporation occurs.
2.2.11 Canopy Interception
When a vegetated canopy is present, snow can become trapped by the branches and foliage of
the canopy, potentially inhibiting the trapped snow from reaching the snowpack on the ground
surface. While suspended in the canopy, snow is susceptible to the same physical processes as
snow on the ground surface and is not only significant to the overall energy and mass balance
equations but is also subject to its own energy and mass balances. Falling snow is not the only
method for which snow can become trapped within a canopy. Horizontally blown snow can also
become a significant source of trapped snow. Hedstrom and Pomeroy (1998) estimated the
snowfall canopy interception, I, as can be seen in Equation 2.20:
[2.20]
28
where csuc is a dimensionless snow unloading coefficient found to be 0.697, I* is the maximum
snow load (kg m-2
), I0 is the snow load (kg m-2
), Rs is the snowfall for a unit of time, and Ccan is
the canopy coverage fraction.
The maximum snow load can be determined using Equation 2.21; where Sp is a tree species
coefficient, LAI is the leaf area index, and ρs(fresh) is the fresh snow density (kg m-3
).
[2.21]
For the purpose of this thesis, canopy interception is considered negligible. Even though the field
site is bordered by a small forest on one side and a thin treeline on another, the model has
difficulty simulating the effects from these canopies due to the exclusion of canopy interception
algorithms in the modules being used.
2.2.12 Blowing Snow
Blowing snow is a very important process as it is the main form of snow redistribution on the
ground and within the atmospheric boundary layer. This redistribution of snow can and will have
an effect on other processes such as the sensible and latent heat fluxes. It can be divided into two
parts: saltation and suspension. Sublimation also plays an integral role in blowing snow transport
and further information will be covered in the next few sections devoted to blowing snow and the
Prairie Blowing Snow Model.
2.3 Blowing Snow and the Winter Moisture Budget
The redistribution of snow by wind is a very important concept for any hydrological research
project located within the cryosphere. Wind redistributes snow by eroding it from areas of high
wind speed, such as ridge tops and windward slopes, and deposits it in areas of lower wind
29
speed, such as the lees of ridge tops, vegetation stands, and topographic depressions (Benson and
Sturm, 1993; Pomeroy et al., 1993; Liston and Sturm, 1998; Sturm et al., 2001a; Liston et al.,
2002). When the prevailing winds constantly come from the same direction, a pattern of
heterogeneous snow drifts occur in the same location year after year. This redistribution can lead
to patterns of environmental conditions and ecosystem properties. Affected properties include net
solar radiation, chemical inputs, meltwater distribution, rock weathering, pedogenesis,
decomposition and mineralization, animal habitat, and vegetation (Hiemstra et al., 2002).
Snow is a loose surface, allowing saltation and suspension to act as the primary mechanisms for
distributing it by wind (Kobayashi, 1972; Male, 1980; Takeuchi, 1980; Schmidt, 1982, 1986;
Pomeroy, 1988; Pomeroy and Gray, 1990). Empirical and analytical relationship between wind
speed and blowing snow transport rate developed by these researchers can be found within their
snow-transport models and those developed by others (Tabler and others, 1990; Liston and
others, 1993a; Bintanja, 1998a,b; Sundsbø, 1997; Purves and others, 1998). Others have shown
that sublimation can be important, reducing the snowcover water balance by a significant
fraction under certain conditions (Goodison, 1981; Benson, 1982; Benson and Sturm, 1993;
Pomeroy and others, 1993, 1997). Modelling provides an alternative method for representing
winter wind-transported processes over various landscapes. It offers an opportunity to evaluate
the relative importance of driving variables, and producing scenarios based on alterations in
these variables. Model outputs can in turn be distributed across realistic terrain and vegetation
representations to produce landscape models that integrate key blowing snow processes
(Pomeroy et al., 1997, Liston and Sturm, 1998). The following section explains the winter
moisture budget and some of the associated problems that occur when attempting to acquire
information that can be used in a blowing-snow transportation model.
30
2.3.1 The winter moisture budget
When the temperature falls consistently below freezing, the simplest way to describe the winter
moisture budget (in the absence of any net horizontal transport) is: snow-water-equivalent depth
(D) equals precipitation (P) minus sublimation (S) (Liston and Sturm, 2004, equation 2.22):
[2.22]
The use of this equation is based on a few assumptions including the fact that spatial variation in
erosion and deposition are negligible and that sublimation is easily modelled or measured.
2.3.1.1 Precipitation
Precipitation accumulates on the ground, building a snow cover that affects atmospheric and soil
temperatures by moderating conductive, sensible, and latent heat energy transfers between the
atmosphere, snowcover, and ground (Hinzman et al., 1998; Nelson et al., 1998; Liston, 1999).
Precipitation on the other hand has proven to be quite challenging to measure accurately. Solid
precipitation generally falls when it is windy and windy environments can pose significant
underestimation in solid precipitation amounts (Larson and Peck, 1974; Goodison et al., 1981;
Benson, 1982; Yang et al., 1998, 2000), however, in some extremely windy conditions, blowing
snow can be caught by precipitation gauges, causing an overestimation (Yang and Ohata, 2001).
Yang et al. (1998) stated that;
“Even the most complex and advanced shielded gauges, such as the WMO Solid Precipitation
Measurement Intercomparison Project‟s „octagonal vertical Double Fence Intercomparison Reference‟
(DFIR), are unable to measure the true precipitation (liquid or solid) and require corrections for wind
speed.”
These corrections are not that large but are necessary. The standard unshielded 8-inch
precipitation gauge used by the National Weather Service (NWS) has an undercatch of nearly
31
75% when exposed to windy environments (Goodison et al., 1981; Benson, 1982; Yang et al.,
1998, 2000). Others have shown that another form of gauge, the shielded Wyoming gauge, has
an undercatch of 6% for snowfall in non-windy conditions and 55% for blowing snow (Rechard
and Larson, 1971; Benson, 1982; Goodison et al.,1998; Yang et al., 2000). This is not only
important at the local scale but also at the regional and global scale. Precipitation gauge networks
are a crucial component to larger scale projects but there are very few networks that contain a
large amount of gauges. This means that one gauge is responsible for covering a very large area
which would induce a significant amount of potential error. There is some advocacy to increase
the number of monitoring stations that record precipitation across the Arctic but the reality of is
that this number is actually decreasing rather than increasing (Shiklomanov et al., 2002).
2.3.1.2 Snow depth measurements
In addition to the problems associated with precipitation gauges, there are also issues that arise
when attempting to record snow depth. The most accurate method of acquiring snow depth
measurements is to measure the amount of snow on the ground. Direct measurement using snow
courses (Pomeroy and Gray, 1995) and watershed surveys (Elder et al., 1991) can be effective
but time consuming, not to mention costly. It can even be very dangerous in certain terrain (e.g.
in avalanche zones). Liston and Sturm have found that due to the occurrence of blowing snow
and drifting snow, the snow depth and SWE distribution can be highly heterogeneous (Liston
and Sturm, 2002; Sturm and Liston, 2003). Both topography and vegetation play an important
role in this distribution and in many cases; require the use of models to help finalize the snow
depth amounts. Snow distribution is easier to estimate in flat terrain where there are no drift traps
present. It is assumed that the amount of snow being removed from one location due to blowing
snow and drifting will be countered by the same amount being brought in by the same
32
mechanisms. Under these conditions, Equation 1 is valid. Otherwise, the use of blowing snow
models are important in acquiring values for snow depth in any area, large or small.
2.3.1.3 Sublimation
If snow is not caught in drift traps, and if the blowing snow event lasts long enough and the air
remains unsaturated, then particles can sublimate away. Tabler (1975) introduced the concept of
a particle transport distance – the distance an average-sized snow/ice grain can travel before it
completely sublimates away. Tabler (1975) found that for Wyoming, the average transport
distance was 3km. Following Tabler‟s methods, Benson (1982) found that this distance decreases
to 2-3km for the Arctic. There appears to be two separate schools of thought when it comes to
snow sublimation. One school of thought states that the highest rates of sublimation occur when
the snow particles are moving. Schmidt (1982) states that when the particles are in the wind
stream, their high surface-area to mass ratios and high ventilation velocities are responsible for
the high rates of sublimation. This research also demonstrated that these rates are as much as two
orders of magnitude higher than those for static snow under similar conditions (Schmidt, 1982).
The dependence of blowing snow sublimation rates on air temperature, humidity deficit, wind
speed, and particle size distribution, can be seen in the works of Tabler (1975), Lee (1975),
Schmidt (1982), and Pomeroy and Gray (1995). Schmidt‟s work has led to the creation of
blowing snow models such as the Prairie Blowing Snow Model (Pomeroy et al., 1993) and
SnowTran-3D (Liston and Sturm, 1998) to name a few. These models base their estimation of
sublimation as a direct result of wind transportation and do not include static snow sublimation
rates.
33
Contrary to this school of thought, other studies have shown that blowing-snow sublimation is
not as important as sublimation from a static snow surface (Mann et al., 2000; Déry and Yau,
2001, 2002; King et al., 2001). In these studies, it is suggested that the atmospheric boundary
layer (ABL) quickly becomes saturated under blowing snow events and is therefore unable to
promote further ABL sublimation. Déry and Yau (2002) have found that static snow sublimation
rates were 5-10 times higher than those found in blowing snow conditions.
Liston and Sturm (2004) suggest that perhaps there may indeed be two different sublimation
regimes, with the interaction between the ABL and the overlying air mass determining which
regime dominates. They suggest both a “humid” regime and a “dry” regime. A “humid” regime
exists when the ABL is unable to mix with the overlying air mass and that the air is already
saturated. In this case static-snow sublimation is the dominate regime. Contrary to this, a “dry”
regime exists when the ABL is able to continuously mix with an overlying dry air mass, wicking
away any moisture from the near surface layer of air and from snow particles. In this case,
blowing-snow sublimation is the dominant regime (Liston and Sturm, 2004).
2.4 Summary
This chapter is focussed on providing background information about the physical properties of
snow and energy and mass exchanges through water. Information, importance, and data
collection of the physical processes of snow including precipitation, density, snow depth, and
snow water equivalent are all discussed. Energy and mass balance component models are also
discussed. Within the energy balance components there is a focus on the radiation budget as it
pertains to snow as well as a comparison of several different energy balance equations from
multiple sources. Mass balance components include changes to the snowpack through
34
sublimation, evaporation, and condensation, canopy interception, and blowing snow. Blowing
snow is a very important component to this thesis and is further discussed as it pertains to the
winter moisture budget. Multiple trains of thought exist as to what is actually occurring in the
atmospheric boundary layer and these trains of thought are discussed.
35
Chapter 3
The Models
3.1 The Prairie Blowing Snow Model
The prairie blowing snow model (PBSM) is an ensemble of physically based blowing snow
transport and sublimation algorithms which calculates the distribution of seasonal snowfall in
agricultural areas of the Canadian prairies. Snow transport is divided into two parts: saltation –
the movement of particles in a „skipping‟ action just above the snow surface, and suspension –
the movement of particles suspended by turbulence in the atmospheric layer extending to the
surface boundary-layer. Sublimation rates are calculated for a column of saltating and suspended
blowing snow extending to the top of the boundary layer (Pomeroy et al., 1993). The model was
designed to be able to predict: 1) mean vertical profiles of snow transport flux; 2) the effect of
grain stubble height on blowing snow transport and sublimation losses from snow cover; 3) the
effect of land use and unobstructed fetch distance on blowing snow transport and sublimation
losses from snowcovers. The process algorithms used that make up the model make use of
readily available meteorological information such as wind speed, temperature, humidity
measured at a single height, occurrence of blowing snow and land use information.
3.1.1 Saltation
The occurrence of high winds over a loose surface can allow particles to become induced into
several types of aeolian movement: saltation, suspension and, in some instances, surface 'creep'
(Kind, 1990). Saltation is the process by which particles are transported horizontally by bouncing
along the surface and is usually initiated by the collision of one particle into another (Bagnold,
1941) (Fig. 3-1). The distance travelled by a saltating particle is determined in part by the mean
flow of the fluid, the particle size and surface conditions (Pomeroy and Gray, 1995).
36
Figure 3-1: Diagram showing the processes of saltation and suspension of sediments into the atmosphere (adapted from
Greeley and Iversen, 1985
Pomeroy and Gray (1990) found that the expression for the vertically integrated saltation
transport rate, Qsalt (kg m-1
s-1
), used in the PBSM is as follows
[3.1]
where Csalt is an empirically derived constant found to equal to 0.68 ms-1
, ρ is the air density (kg
m-3
), g is the acceleration due to gravity (m s-2
), u* is the atmospheric friction velocity (m s
-1) and
the subscripts n and t refer to the friction velocity (shear stress) applied to the non-erodible
surface elements (e.g. rocks and bushes that are protruding through the snow) and to the snow
surface, respectively, at the transportation threshold. This friction velocity is dependent on the
wind speed and the surface roughness and can be expressed as follows
[3.2]
where k is von Kàrmàn‟s constant (0.4), u(z) is the wind speed at height z and z0 is the
aerodynamic roughness height. Further explanations and examples of the threshold velocities of
non-erodible and snow surfaces can be found in Pomeroy et al. (1993). McEwen (1993) found
37
that, close to the surface, the wind profile is modified because some of the sheer stress is carried
by the saltating or suspended particles. As well, the apparent roughness length is also modified.
Pomeroy (1988) found that the roughness height for blowing snow over complete snowcovers
can be expressed as follows
[3.3]
in which Cz is a dimensionless coefficient found equal to 0.1203 for prairie snowcovers, Cst is a
coefficient equal to 0.5m, Nst is the number of vegetation elements per unit area and Ast is the
exposed silhouette area of a single typical vegetation element which can be expressed as the
product of the stalk diameter and the exposed stalk height (total stalk height minus snow depth).
As an example, a typical value of Nst for a wheat field in Saskatchewan is 320 stalks m-2
(Pomeroy et al., 1993). Under high threshold conditions an efficient, particle-surface interaction
enhances saltation transport at high wind speeds but inhibits transport at low wind speeds. This
leads to an approximately linear relationship between wind speed and the saltating transport rate.
3.1.2 Suspension
Suspension of snow can only occur once particles that are already saltating have reached a
terminal velocity that is balanced by the upward-moving winds of the atmospheric boundary
layer due to turbulence. Calculating the rate of transportation for suspended snow can be found
by integrating the mass flux over the depth of flow, which can be classified as the area between
the top of the saltation layer to the top of the surface-boundary layer. Schmidt (1982) defined the
mass flux as the mass concentration multiplied by the mean downwind particle velocity. On
average this velocity is equal to the velocity of the parcel of air. From the equation for u*, the
transportation rate of suspension, Qsusp (kg m-1
s-1
), is
38
[3.4]
where h* and zb are the lower and upper boundaries of the suspension layer, respectively, n(z) is
the mass concentration of suspended snow (kg m-3
) at height z (m). Further information and
calculations of n(z) can be found in Pomeroy and Male (1992) and Pomeroy and Gray (1990).
The upper boundary height, zb, is assumed to be dependent on the fetch over uniform, mobile
snow, however in the PBSM code there is a 5m upper limit that is often imposed for snow
transport calculations. Pomeroy (1998) suggested that snow particles that have been lifted to
heights above 5m are unlikely to settle back to the surface before sublimation removes much of
their mass. Therefore, for „surface hydrological purposes‟, only the mass flux below 5m heights
are considered when calculating the snow transport rates. In order for flow to fully develop, a
minimum fetch distance of 300m is required. Knowing this, the modelled equation for zb can be
written as
[3.5]
where x is the downwind distance from the beginning of the fetch over which the surface
roughness and the aerodynamic roughness, z0, can be considered uniform. This equation is a
modified version that now incorporates the value of 0.3, which was taken from Takeuchi (1980)
as the value for the top of a plume of diffusing particles at an elapsed time, zp(t). Following
Pomeroy and Male (1992), the estimations for the value of h* can be expressed as
[3.6]
where ch is a coefficient found equal to 0.08436 m-0.27
s1.27
.
Suspension transport increases as a power function of wind speed (Pomeroy, 1988). While the
presence of exposed crop stubble increases the wind speed required to attain particle suspension,
39
an increase in turbulence due to this exposed stubble also increases the suspended transport rate
for a given wind speed above this limit.
3.1.3 Sublimation
Sublimation also plays a key role in blowing snow transportation rates. It can act as a significant
source of water vapour and as a sink for sensible heat in the air. It may also lead to a decrease in
size (radius) and mass of snow and ice particles, resulting in a reduction in their drag
coefficients. This means that in real terms, the problem of blowing snow can incorporate a
multitude of particle sizes and therefore should be dealt with in such a manner. The model
however, treats the problem with a mean particle size from a certain distribution of particles in a
steady-state atmosphere. Pomeroy and Gray (1994, 1995) have argued that, in the Canadian
Prairies, up to 75% of the annual snowfall over a one-kilometre fallow field is eroded by wind,
and that, typically, up to half of this amount is sublimated before deposition occurs. According to
Schmidt (1972, 1991), the rate of sublimation of a snow particle may be modelled by a balance
between radiative energy exchange, convective heat transfer to the snow particle, turbulent
transfer of water vapour from the snow particle and the consumption of heat by sublimation. If
we assume thermodynamic equilibrium, the rate of change of mass with respect to time can be
expressed as follows
[3.7]
(for more information on the derivation of this equation, see Schmidt 1991) where r is the radius
of a snow particle containing mass, m; σ (dimensionless and negative) is the water vapour deficit
with respect to ice (e-ei)/ei, where ei is the saturation vapour pressure (svp) over ice, and
approximately equal to relative humidity minus one (RH-1); Qr is the radiant energy received by
40
the particle; λs is the latent heat of sublimation (2.838 x 106 J kg
-1); M is the molecular weight of
water (18.01 kg kmol-1
); R is the universal gas constant (8313 J kmol-1
K-1
); D is the diffusivity of
water (m2s
-1); Ta is the ambient air temperature; ρsat is the saturation density of water vapour (kg
m-3
); Ka is the thermal conductivity of air (W m-1
K-1
); and Nu and Sh are the Nusselt and
Sherwood numbers, respectively. The Nusselt number is a dimensionless number that represents
the ratio of convective to conductive heat transfer. The Sherwood number is also a dimensionless
number (also referred to as the mass transfer Nusselt number) which represents the ratio of
convective to diffusive mass transport. Lee (1975) found that adjacent to a blowing snow particle
in a turbulent atmosphere Nu is identical to Sh (Nu≡Sh). Both terms are dependent on Reynolds
number, Re(r,z) as
[3.8]
in which,
[3.9]
where Vr is the ventilation velocity and v is the kinematic viscosity of air (1.88 x 10-5
s-1
). In the
suspension layer, one could ignore the effects of turbulence on Vr (Schmidt, 1982b; Pomeroy and
Male, 1986) resulting in Vr being equal to the terminal velocities (ws) of the particles expressed
as
[3.10]
In the saltation layer, the ventilation velocity is divided into vertical (Csalt u*) and horizontal
components (2.3ut*)(Pomeroy and Gray, 1990). We already know the value of Csalt from
Equation 2 as 0.68, thus Vr can be written as
[3.11]
41
In terms of order of magnitude, Pomeroy (1988) argues that “the speed of the saltating particles
relative to the wind speed is equal to the speed of the saltating particles relative to the surface”
The rate of change in mass of a particle requires the specification of the undersaturation of water
vapour, σ(=RH-1) given by
[3.12]
where σ2 is the undersaturation at z = 2m when there is a decrease in relative humidity with
increasing height during blowing snow. When the opposite occurs, Déry and Taylor (1996) have
shown that the undersaturation can be given by
[3.13]
Taken from Déry and Taylor (2006), the sublimation rate (negative) per unit area of snowcover,
qsubl (kg m-2
s-1
), can be determined by integrating the sublimation loss rate coefficient [csubl(z)]
for the entire column of blowing snow extending from the snow surface to the top of the
suspension layer, multiplied by the frequency of a certain particle size and its mass, over the
particle spectrum and over height. Giving us
[3.14]
where dr is the particle size increment (m) and N is the total number of particles per unit volume.
Further information on the sublimation loss coefficient, frequency distribution, and particle
radius can be found in Pomeroy et al. (1993) and Déry and Taylor (1996).
3.1.4 Erosion and Deposition
The PBSM is also able to calculate the rate of surface erosion and deposition at distance x,
downwind of the leading edge of a fetch qv(x,0). This rate is established by the net mass of snow
entering or leaving a controlled volume of atmosphere, which extends from the snow surface to
42
the top of the surface boundary-layer for blowing snow, in x and z directions and through
sublimation occurring within this volume as well (Fig 3-2).
This erosion/deposition rate can be expressed as follows
[3.15]
in which the vertical flux at the top of the controlled volume, qv(x, zb), is equal to the negative of
the snowfall rate. In order for flow to fully develop, the surface erosion rate must equal the
sublimation rate minus the snowfall rate and will develop under invariant atmospheric and
surface conditions so long as there is an adequate fetch of mobile snow. The amount of fetch will
vary depending on land use and land cover. Pomeroy (1988) suggests a distance of 500m for full
development of flow to a height of 5m. Deposition on the other hand, occurs when the surface
roughness is great enough to, or there are topographic depressions that, decrease the wind speed
and the saltation and the suspension rates of transport, or when the snowfall is greater than the
surface erosion rate.
Figure 3-2. Cross sectional view of controlled volume of atmosphere extending from the snow surface to the top of the
boundary-layer for blowing snow (Pomeroy et al., 1993)
Within CRHM, the snow mass balance is dealt with slightly differently than the original model.
The snow mass balance for an HRU is due to the distribution and divergence of blowing snow
43
fluxes in and around said HRU. With a fetch, x (m), the following expression for mass balance
can be drawn over an HRU,
[3.16]
where dSWE/dt is the surface snow accumulation rate (kg m-2
s-1
), P is the snowfall rate (kg m-2
s-
1), p is the probability of blowing snow occurrence within the HRU, F is the downwind transport
rate (kg m-2
s-1
), E is the snow surface sublimation rate (kg m-2
s-1
), EB is the blowing snow
sublimation rate (kg m-2
s-1
), and M is the melt rate (kg m-2
s-1
). Proper application of the blowing
snow algorithm requires every term to be solved for. This is why PBSM is coupled with MSM in
this thesis. Nipher snowfall gauge undercatch is corrected for in the PBSM module and SWE
accumulation is calculated as a residual of snow transport, snowfall, and sublimation rates. The
other terms are found when linked to a snowmelt module. Interval data for temperature, relative
humidity, and wind speed are used to calculate the transport and sublimation of blowing snow.
Using a unique parameterization scheme of employing cascading HRUs, PBSM, as implemented
within CRHM, enables the parameterization of the flow of snow transport from HRU to HRU.
Snow is redistributed amongst HRUs by basing it upon snow transport calculations, HRU size,
vegetation characteristics, and a distribution factor, Dp. By implying the distribution factor,
PBSM allocates blowing snow transport from areas that are aerodynamically smoother (windier)
to areas that are aerodynamically rougher (calmer) within a basin. The distribution factor value
ranges from 0 to 10, 10 being the roughest (Fang and Pomeroy, 2009).
44
3.2 Minimal Snowmelt Model
In order for PBSM to work properly it needs to be coupled with a snow melt model. CRHM has
a few different melt modules to choose from but the minimal snowmelt model (MSM) was
chosen for this thesis based on its simplicity and its ease of use using the available collected
meteorological data.
The MSM module is based from Essery and Etchevers, 2004. It is a simple snow model with
only three adjustable parameters (fresh snow albedo, albedo decay rate for melting snow, and
surface roughness length). It performs the energy and mass balances with a focus on the surface
of the snowpack. Changes in the internal snowpack energy, energy from precipitation, and
energy from the ground are all neglected. It is driven by average inputs of incoming shortwave
(K↓) and longwave (L↓) radiation respectively, air temperature, specific humidity (Q1), wind
speed (u), and snowfall rate (Rs). Surface pressure (Ps) and the measurement height (z1) both
must be specified as well.
MSM follows common procedures used in snow models and land surface schemes to calculate
radiant and turbulent exchanges. Surface fluxes of sensible heat (H) and latent heat (LE)
exchanges and can be seen as follows,
[3.17]
and
[3.18]
45
where ρ and Cp are the density and heat capacity of air respectively, Qsat (Ts,Ps) is the saturation
humidity at the snow surface temperature (Ts) and pressure (Ps), CH is a surface exchange
coefficient. Net radiation (R) absorbed by the snow surface is calculated by
[3.19]
where α is the snow albedo and σ is the Stefan-Boltzmann constant.
MSM also deals with albedo decay and atmospheric stability. Further information about the
above as well as the derivation for CH can be seen in Essery and Etchevers, 2004.
Due to the neglecting of heat fluxes within the snowpack, heat advection from precipitation, and
the substrate, the energy balance becomes
[3.20]
where λs and λf are the latent heats of sublimation and fusion respectively. M is the melt energy
(W m-2
). The mass balance is then calculated following
[3.21]
3.3 Summary
This chapter provides a brief synopsis of the Prairie Blowing Snow Model and the Minimal
Snowmelt Model. It highlights the key equations and derivations from the models as they help
lead to a better understanding of the experiments of this thesis. PBSM is a collection of
physically based blowing snow transport and sublimation algorithms and is used to calculate
transportation rates in the forms of saltation and suspension as well as sublimation rates. The
model also calculates erosional and depositional rates with the aid of the snowmelt model MSM.
46
MSM is a simplified snowmelt model that ignores internal energy exchanges within the
snowpack, energy from precipitation, and energy from the ground. This simplified model is
easily coupled with PBSM using the collected met data and provides the missing variables to
complete a mass balance equation that includes blowing snow fluxes. Both PBSM and MSM are
modules found within the 6.0 platform of CRHM which is the main modelling platform used in
this thesis.
47
Chapter 4.
Methods
4.1 Study Site
The study site for this thesis project is located on a small agricultural farm within the Strawberry
Creek watershed (0.4054 km2) which is about 15km northeast of Waterloo, Ontario, Canada
Figure 4-1: Location of Strawberry Creek field site
48
(43° 33‟ 1”N, 80° 23‟ 24”W). This domain can be seen Fig 4-1 and Fig 4-2. Strawberry Creek is
a first order stream that flows into Hopewell Creek and eventually flows into Lake Erie through
the Grand River. The Grand River is the largest catchment basin in southwestern Ontario with a
total flow collection of approximately 6800km2 (Chapman and Putnam, 1984). Figure 4-3
illustrates the Grand River catchment.
The physiography of Strawberry Creek was shaped by late Quaternary processes and is located
in an area referred to as the Guelph Drumlin field (Chapman and Putnam, 1984). Glacial till is
the predominant sub-surface physiology in this area and is assumed to be comprised of
approximately 50% sand, 35% silt, and 15% clay (Chapman and Putnam, 1984). The landscape
is predominantly gently rolling till plains which primarily consist of agricultural fields and very
little pasture. The dominant field crops in the area consist of hay, corn (for grain), soybeans, corn
(for silage), and winter wheat. Several eskers and moraines are located in this region as well
(Karow, 1968). Further information about the physiography, soil structure, vegetation, and
human development of this area can be seen in Chapman and Putnam (1984), Harris (1999), and
Karrow (1974, 1993). The purpose of this subsection is to provide a simple overview of the study
site as it pertains to the over-land flow of wind-transported snow.
The farm (0.4km2) is located just outside the small town of Maryhill. It consists of three separate
vegetated fields (N, NE, SW), the creek running SE through the centre of the farm, and a farm
house and barn located in the centre of the land plot. The N and SW fields are separated from the
NE field by the creek and the N and SW fields are separated by the farmhouse and its driveway.
The N and NE fields were tilled in the late fall, and are therefore unvegetated in the winter and
have small rows of raised earth ridges (~5cm) as a result from the tiller. The SW field has a
winter grass crop with an average height of 10cm.
49
a)
c)
e)
g)
b)
d)
f)
h)
Fig 4-2: A 360 view of the field site from eight cardinal directions. a) Northwest, b) North, c) Northeast, d) East, e)
Southeast, f) South, g) Southwest, h) West.
50
The topography is gently sloping towards the creek with roughly a 9m difference in elevation
between the SW and NE corners to the creek bed (336-345m). There is also a gentle hill located
in the centre of the SW field. The creek is narrow, roughly 1.5m deep and 2m wide under bank-
full conditions and has a general U shape. Dredging of the creek in the past has increased the
Figure 4-3: Grand River watershed (GRCA, 2008)
51
height and steepness of the banks and has also altered the riparian zone on either side.
This study site was chosen for several reasons:
1) It is a good representation of prairie-like conditions in southern Ontario. This is important as
the focus of this thesis is to test the model, which largely consists of the Prairie Blowing Snow
module, in a small, local catchment under different climatic conditions.
2) It is located in an area that is in closer proximity to the University of Waterloo so that it is
easy to get to for the purpose of performing multiple snow courses and data collection over the
entire snow season.
3) A good working relationship between the land owners, farmers and the Universities of
Waterloo and Wilfrid Laurier is already present, making accessibility straightforward.
4.2 Digital Imagery and Data
Digital data coverage for Strawberry Creek included orthoimagery, contour mapping (2m
resolution), road and water networks, and township field boundary maps. All of the data were
collected from the Grand River Conservation Authority‟s Grand River Information Network
(GRIN) (GRCA, 2008), and was used in ArcGIS 9/ArcView version 9.3 Geographical
Information System (GIS) (Environmental Systems Research Institute, Inc. [ESRI], Redlands,
CA). The orthoimagery was collected as a series of digital aerial photography in the spring of
2006 as a larger project named the South West Ontario Orthophotography Project (SWOOP).
Tiles 548_4822 and 548_4820 were used in this project and have a ground pixel size of 30cm
with an estimated positional accuracy of +/-1 metre.
52
4.3 Meteorological data
Half-hourly measurements of windspeed and direction, temperature, relative humidity,
precipitation (rain), snow depth, solar radiation, and air pressure, were taken from a 3m
meteorological tower which was located in the centre of the SW field (as seen in Fig. 1-1). Data
was stored on a Campbell Scientific CR1000 data logger and was uploaded using Campbell
Scientific‟s LoggerNet software package. Error free solid precipitation (snow) is difficult to
obtain (see section on winter moisture budget). Therefore, in order to achieve a value of this
precipitation, snow depth was recorded by the sonic snow depth sensor for time series analysis.
If any significant increase in depth occurred, it was recorded as an increase in precipitation.
Snowfall amounts were generated by examining the difference between precipitation values on a
daily basis and them added together to create a daily snowfall amount. All of the collected
meteorological data was assumed to be consistent across the entire study domain. Table 4-1
demonstrates all of the sensors used on the met tower and their purposes. The meteorological
observations were used to drive the model for the period of 21 November 2008 to 12 February
2009.
Meteorological Condition Instrument
Wind Speed and Direction 05103-10 RM Young wind monitor CSC Spec
Temperature and Relative Humidity HC-S3-XT relative humidity and Air temp probe
Solar Radiation CNR1 KIPP and ZONEN net radiometer sensor
Precipitation (rain) TE525M Texas Instrument tipping bucket
Barometric Pressure 61205V RM Young Barometric pressure sensor
Snow Depth SR50A Sonic ranger 50 KHz module
Table 4-1: List of selected meteorological instrumentation
53
Over the entire winter season there were two significant melt periods where the snow cover
completely melted away except in areas of significant drifting. The first occurred in late
December, the second occurred in early February. Both melt periods were the result of a
combination of warmer temperatures and rain events. Due to instrument malfunction of the
SR50a sonic sensor, data from after the second severe thaw period (Feb. 12/09) was discarded.
This truncated the entire data set to only 83 days.
4.3.1 Ultrasonic snow depth sensors vs. traditional snow measurement techniques
Ultrasonic snow depth sensors (USDS) have been around since the early 1980s (Goodison et al.,
1984). They send out a sound pulse (50 kHz) and measure the time it takes the pulse to reach the
ground and return to the sensor. The pulse is projected downwards over a cone of 30 and for
accurate measurement it is imperative that there are no interferences between the sensor and the
ground surface. The time for the pulse to return to the transducer in the sensor is adjusted for the
Figure 4-4: View of meteorological tower looking south towards the town of Maryhill, Ont.
54
speed of sound in air based on measured air temperature, and the timing is converted to a
distance via internal algorithms. To adjust the speed of sound in air (Vsound) in meters per second
for the ambient air temperature (Ta) in kelvins, the following equation is applied:
[4.1]
The distance the sound pulse travels decreases as snow accumulates on the ground, thus reducing
the time for the pulse to return to the sensor.
Traditional snow measurements consist of gauge precipitation, snowfall, and snow depth. Gauge
precipitation is defined as the liquid equivalent obtained by a nonrecording/recording, standard
precipitation gauge. As is mentioned in the winter moisture budget section of this thesis, gauge
precipitation is greatly affected by wind speed and direction and can lead to erroneous values
obtained for evaluation. Snowfall is defined as the maximum accumulation of new snow since
the last observation and is customarily measured manually with a ruler. Snow depth is defined as
the total depth of snow on the ground at the time of observation and indicates both old and new
snow on undisturbed surfaces. The measurement of snow depth may be the average of several
total depth measurement to obtain a representative sample (NWS, 1996).
USDS measurements are done with respect to manual measurements which are assumed to be
„ground truth‟. Uniformity and consistency in manual measurements are difficult to attain with
any data collector. There is an inherent uncertainty in manual measurements due to the fact that
snow melts, settles, blows, and drifts and does not accumulate uniformly on the ground.
Depending on time of day, the frequency, the measurement surface, the extent of nonuniformity
in snow accumulation, and overall care and detail of the individual observers, some variation in
55
manual observation is to be expected. According to Ryan et al. (2008), there are no known
studies that have attempted to quantify this uncertainty in terms of measurement error, but they
estimate it to be in the magnitude of ± 25%.
The choice to use a Campbell Scientific SR50a sonic sensor to derive solid precipitation values
over traditional measurement techniques was made in part for the ease of obtaining an automated
daily snow depth measurement based on hourly readings which can be personally monitored.
Obtaining a manual snow depth measurement on a daily basis at the field site for the entire
season was feasibly impossible. A daily measurement of snow on the ground was manually
recorded every morning at the Waterloo-Wellington International Airport located in Breslau, 10
km to the southwest but due to any number of potential issues mentioned above, this data was
not used as an input in any model runs for this thesis. A comparison between the SR50a data
from Strawberry Creek and the manual snow depth data from the airport is seen in Fig. 4-5
below. The average seasonal difference between the two data sets was approximately 8.0 cm.
Figure 4-5: Comparison of seasonal snow depth measurements from the automated SR50a sensor at Strawberry Creek
(dashed line) and the manual measurements from the Waterloo-Wellington International Airport (solid line).
0.000.050.100.150.200.250.300.350.400.450.50
21
/11
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08
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08
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08
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Sno
wd
ep
th (
m)
SR50a W-W
56
4.3.2 Meteorological data pre-processing in order for proper model runs
As with many models, the CRHM platform requires specific formats of input data. Therefore, in
order to correctly run the model some of the meteorological data format had to be pre-processed.
Time and date stamps were combined into a decimal value, solar radiation was split up into
incoming and outgoing short and longwave radiation, the windspeed was adjusted from a 2 m
reference height to a 10 m reference height, solid precipitation was averaged on a daily basis, and
the vapour pressure was derived within the model using an observation filter from values of
temperature and relative humidity. Data from the SR50a sonic ranger was only used if it had a
signal quality between the range of 152 to 210. Signal quality of 151 and below resulted in the
sensor‟s inability to read distance. Signal qualities between 211 and 300 and 300+ had reduced
echo signal strength and high measurement uncertainties respectively, and were therefore
discarded. Any missing data was replaced with the preceding data of good quality.
4.4 Snow Surveys
A systematic linear transect sampling strategy was adopted to sample the mean, variance, and
distribution of snow throughout the entire field site. Snow depth surveys were conducted over
the winter of 2008-2009 using a GPS-magnaprobe from Snowhydro®. Surveys were conducted
on a winter storm basis or a bi-weekly basis if no new accumulation of snow had fallen since the
previous storm. Surveys were completed on the days of Dec. 08, in 2008 and Jan. 15, 21, 29,
Feb. 04, in 2009. Gaps in the surveying structure were due to the fact that several melt periods
occurred where there was no longer any snow on the ground surface to be measured. This
occurred twice over the entire season, once in the middle of December and once again in the
middle of February.
57
Initially, only two transects were chosen to cover the entire field site; a NW-SE transect and a
NE-SW transect creating an „X‟ pattern across the site. After much review, it was decided to
include a perimeter transect as well as two more parallel transects (N-S) in order to better
represent snow depth through spatial interpolation. Perimeter transects were labelled in order of
geographical location (ie. Northern, Eastern, Southern, Western, Northwestern) and the interior
transects were labelled numerically (ie. 1, 2, 3, 4). The following diagram (Fig. 4-6)
demonstrates the pattern of snow depth transects used. Snow depths were measured at 5-m
intervals along these transects.
Figure 4-6: Map showing field site and snow depth transects
When using the Magnaprobe, the depth accuracy is ± 3mm if accurately calibrated but this is
conditional on snow conditions, underlying vegetation, and battery power. On several occasions
58
when there were only trace amounts of snow on the ground, no surveys were conducted because
the Magnaprobe was unable to detect these small amounts. The accuracy may be ±3mm but that
is only when there is enough snow at the right density threshold to allow the depth sensor to
move along the rod and record a value. The GPS accuracy (both absolute and relative) has been
shown to be ± 5m but is dependent on atmospheric conditions and satellites availability. This did
not prove to be an issue at this field site. Data from the MagnaProbe is stored on a Campbell
Scientific CR800 datalogger and is downloaded for analysis using Campbell Scientific‟s
LoggerNet software package.
4.5 Model Experiments
In addition to field sampling, PBSM and MSM modules were used within the CRHM model to
estimate the snow accumulation and distribution over the entire field site. The model was driven
with half-hourly averaged air temperature, wind speed, humidity, incoming and outgoing short
and longwave radiation, and daily averaged solid precipitation data during the snow
accumulation period, 21 November 2008 to 12 February 2009, (as was derived from the SR50a
data). It is assumed that all forcing data were uniform across the entire field site. The model runs
were divided into two different methods, lumped and distributed, respectively. Furthermore, the
lumped method experiments were sequentially run at two different scales; point scale and field
scale. The distributed method was run solely at the field scale.
4.5.1 Lumped Model – Point Scale
Initially, the model was run in the lumped format at the point scale using the forcing data from
the meteorological station and then compared to an average of 10 observed snow depth points
59
from the same location and timestamp. Model runs at this scale assume a single HRU
(approximately 0.025 km2).
4.5.2 Lumped Model – Field Scale
Secondly, the model was scaled up in lumped format to the field scale using the same forcing
data and then compared to observed snow depth points from the entire field site for each date of
survey. Model runs at this scale also assume a single HRU (approximately 0.406 km2).
4.5.3 Distributed Model – Field Scale
In order to test the model‟s ability to spatially discretize, the model was then run at the field scale
but in a distributed format. In order to do so, the field site was subdivided into three separate
HRUs named Field 1 (0.183km2), Stream (0.011km
2), and Field 2 (0.212km
2) as seen in Figure
4-7 and Table 4-2, and modelled results are compared to observed snow depth points gathered
from each HRU.
4.5.4 Model Parameters
In order to adapt the model for the Strawberry Creek field site, modifications were made to the
model parameters. Control case parameters include the basin area being set to 0.4054 km2, the
basin and observation elevation being set to 343 m asl, latitude set for 43.5°N, observation
reference height (Zref) set to 2.47m above the ground surface, and the vegetation height set to
0.05m. Due to the rolling terrain of the field site, the blowing snow fetch distance was assumed
to be the PBSM minimum of 300 m. All other parameters were set to default (Table 4-2,
Appendix 1). Based on the literature (Pomeroy et al, 1993) and knowledge of the terrain, the
model snow density was assumed to be 250 kg m-3
. Distributed method parameters include
60
adjusting the HRU areas to those specified above and vegetation heights of 0.1m, 1.5m, and
0.05m respectively for Field 1, Stream, and Field 2. These values were determined based on in
situ observations. The value of 1.5m of vegetation height for the stream was determined to best
represent the combination of the vegetation height in the riparian zone as well as the topographic
depression of the stream itself.
Figure 4-7: Distributed map of CRHM hydrological response units Field 1 (green), Stream (blue), and Field 2 (pink)
Table 4-2 demonstrates all of the model parameters and their values. A definition of each of
these parameters can be found in Appendix 1. Sheltering effects of the farm buildings, driveway,
and garden vegetation were not considered in any of the model runs.
61
CRHM Module
Parameter Lumped Distributed
HRU1 HRU2 HRU3
Bas
in
basin_area 0.4054
basin_name SC
hru_area 0.4054 0.1827 0.01062 0.2121
hru_ASL 0 0 0 0
hru_elev 343 343 343 343
hru_GSL 0 0 0 0
hru_lat 43.5 43.5 43.5 43.5
hru_names HRU Field 1 Stream Field 2
Run_ID 1
OB
S
catchadjust 0 0 0 0
HRU_OBS 1 1 1 1
lapse_rate 0.75 0.75 0.75 0.75
Obs_elev 343 343 343 343
ppt_daily_distrib 1 1 1 1
tmax_allrain 0 0 0 0
tmax_allsnow 0 0 0 0
MSM
_Org
a1 1.08E+07 1.08E+07 1.08E+07 1.08E+07
a2 7.20E+05 7.20E+05 7.20E+05 7.20E+05
amax 0.84 0.84 0.84 0.84
amin 0.5 0.5 0.5 0.5
smin 10 10 10 10
Z0 snow 0.01 0.01 0.01 0.01
Zref 2.47 2.47 2.47 2.47
PB
SM
A_S 0.001 0.001 0.001 0.001
distrib 0 0 1 1
fetch 300 300 300 300
Ht 0.05 0.1 1.5 0.05
inhibit_bs 0 0 0 0
inhibit_evap 0 0 0 0
N_S 320 320 320 320 Table 4-2: CRHM model parameters
Values for the blowing snow distribution factor, Dp, were determined by trial-and-error runs with
the knowledge of geographical proximity and aerodynamic roughness for each HRU.
62
HRU name Area (km2) Vegetation Height
(m)
Blowing snow
fetch distance (m)
Blowing snow
distribution factor
Dp
Field 1 0.183 0.1 300 2
Stream 0.011 1.5 300 10
Field 2 0.212 0.05 300 1
Total field site 0.405 0.05 300 1 Table 4-3: Characteristics of HRU parameters for blowing snow experiments at Strawberry Creek
In Table 4-3, a Dp value of 1 and 2 was assigned to Field 2 and Field 1 HRUs respectively
because they both have low aerodynamic roughness and are typically blowing snow „sources‟. A
Dp value of 10 was assigned to the Stream HRU due to it being a topographic depression with a
high aerodynamic roughness and therefore acting as a blowing snow „sink‟. For the lumped
model experiment, a Dp value of 1 was given for the entire field site.
A schematic diagram depicting the flow of inputs and outputs between the modules within
CRHM can be seen in Fig. 4-8. In addition to the MSM and PBSM modules, basin (BASIN),
observation (OBS) and interception (INTCP) modules were added as they were required for
complete model construction. The BASIN module allows the model user to set the parameters as
required for each HRU being used. Meteorological forcing data is put into the OBS and MSM
modules where it is filtered into specific HRU observations and used for the generation of
snowmelt energy values respectively. The INTCP module is required by PBSM to deal with any
incoming precipitation being held within a canopy. In the case of this thesis, there is no canopy
to deal with therefore, INTCP is negligible and merely acts to change the name of incoming
63
t
rh
ea
u
p
ppt
QSi
Qli
hru_t
hru_rh
hru_u
hru_p
hru_rain
hru_snow
hru_newsnow
net_snow
SWE
t
u
rh
*P
Snowmelt
energy
Figure 4-8: A simplified schematic diagram of the progression of module input
observations through the CRHM model modules.
OBS
INTCP
MSM_Org
PBSM Snow depth
BASIN
64
precipitation between OBS and MSM/PBSM. This is a necessary step in order for the
MSM/PBSM modules to reckognize the precipitation. The *P denotes a backwards PUT variable
which is an input variable that is derived from another module. In this case, the MSM_Org
module requires both SWE and net_snow from PBSM and INTCP before any snowmelt energy
values are generated. Once snowmelt energy values are generated, they are input into PBSM and
a final value for snow depth is achieved.
4.6 Model testing and verification
Initially, model results of snow depth are compared to measured snow depth for each day of
snow surveying and then compared throughout the entire season. This creates a temporal analysis
that enables testing of the model performance on a daily and seasonal basis. Spatial analysis is
accomplished by analyzing the model results between the various scales of modelling. According
to Rykiel (1996), “validation is a demonstration that a model within its domain of applicability
possesses a satisfactory range of accuracy consistent with the intended application of the model.”
In order to uphold this criterion, the purpose, performance criteria and context of the model are
all well defined. The purpose of the model is to simulate the seasonal snow accumulation
occurring at Strawberry Creek during the winter of 2008-2009. The performance criteria include
the production of a quantitative agreement between observed and simulated snow depths. The
model context was limited to the Strawberry Creek field site and the winter of 2008-2009 for
three specific reasons: 1) the vegetation and topography represent a prairie-like condition on a
small scale in as much as the field was not sheltered significantly by trees or relief, 2) the snow
accumulation and melt periods are well defined and easily determined, and 3) the forcing
meteorological data is year specific. Qualitative comparisons were made by visual inspection of
65
modelled and observed results of snow depth in graphical formats. The evaluation of the model
performance is done by three statistical approaches, Root Mean Square Difference (RMSD),
Nash-Sutcliffe coefficient (NS) (Nash and Sutcliffe, 1970) and Model Bias (MB), which are
calculated as:
[4.2]
[4.3]
[4.4]
Where n is the number of samples, SDo, SDs, and are the observed, simulated, and mean of
the observed snow depths, respectively. The RMSD is a weighted measure of the difference
between simulated and observed snow depths and has the same units of measurement. The NS
coefficient measures the model efficiency and MB supports NS by quantifying the model‟s under
and overprediction.
As the number of environmental models have increased over the past few decades, so too has the
need for the development of more precise and accurate estimates of the desired variable(s) from
the model results. This in turn led to an increase in the use of a variety of different statistical
methods assessing accuracy or goodness of fit and error (as seen in recent papers: Fekete et al.,
2004; Cavazos and Hewiston, 2005; Willmott and Matsuura, 2005). Some of the more popular
and widely reported error measures found in the literature include coefficients of correlation
(also known as Pearson‟s product moment correlation; r) and determination (r2) as well as the
root mean square deviation (RMSD). There is much debate over which statistical method
provides the best evaluation of model accuracy and selecting a method can be difficult seeing as
66
how it is based not only on the researcher‟s personal preference but also on the type of model
being used, the method in which the model was calibrated, and the amount of estimated data
points being compared against observed data. W.R. Black (1991) argues that the coefficients of
correlation and determination are measures of relationship or association between estimated and
observed data but they are not the best measure of accuracy or goodness of fit when comparing
model estimates with observed data. Instead, RMSD should be used (Black, 1991). Previous
model experiments using PBSM have included RMSD as one of the main methods of assessing
model accuracy/error and it seemed only fitting to use the same method in this thesis. Even
though RMSD is one of the most widely reported error measures in the literature, it is not
without its own inherent error (see Willmott and Matsuura, 2005). RMSD is not standardized,
making it difficult to look at on its own as a sole measure of model performance. Even though it
demonstrates an amount of average error in the same units as the variables being estimated, this
error value is only a relative term. It is for this reason that other statistical methods were selected
(Nash-Sutcliffe coefficient (NS) and the Model Bias (MB)) in addition to RMSD to demonstrate
the model‟s performance in this paper. NS is widely used and reliable statistic for assessing
goodness of fit of hydrological models. It is very similar to the Pearson product in that the values
of the coefficient give a measure of correlation and can be anywhere between - and +1.
However, unlike the Pearson product, which is theoretically only applicable to linear models that
include an intercept and is greatly affected by model bias, NS can be applied to a variety of
models regardless of model bias (Nash and Sutcliffe, 1970; McCuen et al., 1990, 2006). With
NS, a value of 1 implies that the model perfectly predicts the simulated results compared to the
observed. A value equal to zero indicates that the simulated results are no better than the average
of the observed values. A value less than zero indicates that the observed mean is a better
67
predictor then the simulated results. Therefore, any positive value of this coefficient indicates
that the model has some predictive power and the higher the value, the better the model
performs. Model Bias (MB) is added to support the predictive power of the model as seen in the
Nash-Sutcliffe coefficient. A positive value and negative value of MB indicate overprediction
and underprediction of the model, respectively. Following similar research from Fang and
Pomeroy (2009), an acceptable range of model performance was chosen to be <30% (MB <
0.30).
4.7 Summary
This chapter provides a description of the methodology and modelling approach used in this
thesis. It provides a detailed description and geological history of the study site as well as all of
the data used to map out the study site and snow surveys. All methods of acquiring
meteorological data and the required alterations to this data used in the model experiments are
discussed in length. Snow surveys play a key role in validating the model experiments and this
section describes in full the steps taken to acquire snow depth values across the entire field site
using a GPS-magnaprobe throughout the winter season of 2008-2009. Model experiments as
well as model validation and testing processes are also outlined. The final section justifies the
statistical methods used to assess the accuracy or goodness of fit of the model compared to the
observed data.
68
Chapter 5.
Results
5.1 Field Results
The precipitation pattern at Strawberry Creek during the winter season of 2008-2009 featured a
dry fall and early winter with snow accumulating on the ground in late November. Most of the
snow accumulation in this area occurs between the months of December and March. In some
anomalous years snow accumulation can begin as early as October and remain as late as April.
Most of the snow accumulation occurs due to several large precipitation events throughout the
entire winter season which was the case for this particular winter season. Table 5-1 demonstrates
monthly averages from Strawberry Creek compared to the monthly climatic average from the
Waterloo-Wellington International Airport located in Breslau, 10km to the southwest.
Variable Strawberry Creek Waterloo-Wellington Airport
Nov. Dec. Jan. Feb. Nov. Dec. Jan. Feb.
Temp (C) -2.96 -4.92 -10.39 -5.17 2.30 -3.80 -7.10 -6.40
Rel. Humidity (%) 97.27 98.93 97.86 96.41 87.50 87.00 86.40 83.60
Wind Speed (m/s) 2.62 4.02 2.96 3.23 3.94 4.06 4.28 3.89
Wind Direction (deg) 195.91 212.04 216.85 210.15 225.00 225.00 225.00 270.00
Snow depth (m) 0.05 0.12 0.26 0.36 0.01 0.05 0.12 0.14
Table 5-1: Calculated monthly climatic averages for Strawberry Creek during the 2008-2009 winter season compared to
1971-2000 climatic averages from the Waterloo-Wellington Airport (Environment Canada, 2010)
Climatic averages for temperature, relative humidity, and snow depth were all above the long
term average for the area. Wind speed was not as strong and the wind direction came from a
more southerly direction then the long term average. Collected meteorological data from
Strawberry Creek can be seen in Fig 5-1.
Field observations demonstrate that the Strawberry Creek field site has a characteristic and
predictable snow distribution pattern associated with wind direction, wind speed, topography,
69
Date
Figure 5-1: Corrected meteorological data for Strawberry Creek from November 21, 2008 to February 12, 2009
-25.000
-20.000
-15.000
-10.000
-5.000
0.000
5.000
10.000A
ir T
emp
(°C
)
0.000
20.000
40.000
60.000
80.000
100.000
Rel
ativ
e H
um
idit
y (%
)
0.000
2.000
4.000
6.000
8.000
Win
d S
pee
d (
m/s
)
0
100
200
300
Win
d D
irec
tio
n (
deg
.)
0.00
0.02
0.04
0.06
0.08
0.10
20/11/2008 30/11/2008 10/12/2008 20/12/2008 30/12/2008 09/01/2009 19/01/2009 29/01/2009 08/02/2009
Sno
wfa
ll (m
)
70
and vegetation. During the 2008-2009 winter season, the wind direction typically came from the
south southwest (196 to 217) with an average speed of 3 m s-1
(Table 5-1, Fig. 5-1).
Definitive snow accumulation patterns appeared across the entire field site with drifts occurring
around the edges of vegetation stands and within the creek banks. Scouring occurred in the open
tilled farmlands (N and NE fields) which have a low snow-holding capacity. The SW field had a
slightly higher snow-holding capacity due to the presence of the winter grass crop and therefore
had an increase in snow depth compared to the other two farm fields. The forested borders along
the eastern and western edges of the field site reduced the wind speed substantially, effectively
acting as snow fences, facilitating the accumulation of large quantities of snow (40 to 90 cm
deep). Within the creek banks the snow drifts would completely fill the banks (100 cm) in some
areas and at times, even pile higher, pushing the magnaprobe to its depth limit of 120 cm.
Transect profiles demonstrating snow depth and elevation can be seen in Appendix 2. Fig. 5-2 is
a graphical representation of both the observed snow depth averages on the days of snow
surveying and the modelled snow depth results. It shows the gradual increase in mean field-scale
snow depth from transect data throughout the winter season.
The extreme values in the data are due to snow depth readings from within the creek banks and
drifts along the field site borders. The black circles represent the mean snow depth and the upper
and lower box limits represent the 1st and 3
rd quartiles respectively.
5.2 Model Results
Two modelling approaches were taken in this study: Lumped and distributed. The result of these
approaches can be seen in Fig 5-2 and 5-3 respectively. In both approaches, the model failed to
simulate the early onset of snow until the middle of December and then steadily simulated the
71
seasonal snow accumulation throughout the rest of the test season, which as was previously
mentioned, fell between November 21, 2008 and February 12, 2009. The lumped approach
reached a maximum snow depth of 33.0 cm on two different occasions in the month of January.
In the distributed approach the maximum snow depth from the HRUs Field 1, Field 2, and
Stream were 29.0cm, 28.0cm, and 41.0 cm respectively and occurred at the middle and end of
January.
Figure 5-2 Comparison of averaged model (lumped) and observed snow depth during the 2008-2009 winter season. The
snowfall graph is added to demonstrate snowfall activity throughout the season.
0.00
0.02
0.04
0.06
0.08
0.10
Sno
wfa
ll (m
)
0
0.2
0.4
0.6
0.8
1
1.2
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08
28
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08
05
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08
12
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02
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09
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09
23
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09
30
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/20
09
06
/02
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09
Sno
wd
ep
th (
m)
Modelled SD(m) Observed SD(m)
72
Figure 5-3 Comparison of averaged simulated model snow depth and cumulative snowfall (lines) and observed snow
depth (symbols) for each HRU in the distributed approach over the 2008-2009 winter season.
Accumulation of snow depth in all three HRUs fall predominantly below the cumulative
snowfall line which suggest that the entire field site is subjected to the effects of erosion from the
wind and therefore acts as a source of blowing snow. The only exception to this occurs in the
stream HRU between the end of December and the middle of January. In this case, the stream
acts as a blowing snow sink.
5.3 Comparison of Simulated Model Results and Observed Snow Survey Results at the Point
and Field Scales.
The simulated model results and field observations of snow depth were compared to one another
in three different methods. The first two methods make use of model results from the lumped
modelling approach and compare them to field observations at the point and field scales
respectively. The third method makes use of model results from the distributed modelling
0.0
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Field 1 Stream Field 2 Field 1 Stream 2 Field 2 Snowfall
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approach and compares them with field observations which have been collected from each of the
three HRUs used in the model (Field 1, Stream, and Field 2). Table 5-2, below, displays the
sample size (n value) used in the statistical analysis for the observed snow depth for each day of
survey.
Date
Sample size (n)
Lumped Distributed
Point Scale Field Scale Field 1 Stream Field 2
Dec. 08/08 20 1138 426 44 668
Jan. 15/09 20 856 340 40 476 Jan. 21/09 20 1687 874 112 832 Jan. 29/09 20 1346 614 90 642
Feb. 04/09 20 1280 638 56 638 Table 5-2 Sample sizes of snow depth for each day of snow survey used for statistical analysis
5.3.1 Point Scale Model Results: Lumped
To quantify the performance of the model‟s ability at predicting snow depth at the point scale,
RMSD, NS, and MB we computed for each individual date of snow survey during the 2008-2009
Date RMSD (m) NS MB
Dec.08/08 0.074 -0.097 -0.943 Jan. 15/09 0.051 0.650 0.532 Jan. 21/09 0.022 0.969 0.160 Jan. 29/09 0.004 0.999 -0.027
Feb. 04/09 0.024 0.978 -0.135 Table 5-3 Root Mean Squared Deviation (RMSD), Nash-Sutcliffe coefficient (NS), and Model Bias (MB) for the
comparison of point-scale simulated snow depth in a lumped approach and observed snow depth for each date of snow
transect surveys during the 2008-2009 winter season.
winter season (Table 5-3). RMSD and NS values range from 0.004 m to 0.074 m and -0.097 to
0.999 respectively. The model performs well on Jan. 21/09 and Feb. 04/09 and performs really
well on Jan. 29/09. As was previously mentioned, the model performed poorly in the early half
of the season which is evident in the statistical analysis, most notably on Dec. 08/08 where the
RMSD value was 0.074 m and the NS value was -0.097. The amount of overestimation and
74
underestimation for total snow depth is within 16% for the latter three survey days which is well
within an acceptable range of 30% (Fang and Pomeroy, 2009), however, the model
underestimates by as much as 94% on the first survey day and then overestimates by more than
52% on the following survey day which is unacceptable.
5.3.2 Field Scale Model Results: Lumped
Upscaling from the point scale the field scale is accomplished by including observations from the
entire field site instead of only those which are in close proximity to the meteorological station.
Date RMSD (m) NS MB
Dec.08/08 0.047 0.163 -0.913 Jan. 15/09 0.056 0.600 0.631 Jan. 21/09 0.014 0.977 0.150 Jan. 29/09 0.010 0.995 -0.068
Feb. 04/09 0.023 0.978 -0.147 Table 5-4 Root Mean Squared Deviation (RMSD), Nash-Sutcliffe coefficient (NS), and Model Bias (MB) for the
comparison of field-scale simulated snow depth in a lumped approach and observed snow depth for each date of snow
transect surveys during the 2008-2009 winter season.
By incorporating more field observations, there is an averaging effect on the statistical analysis
(Table 5-4). Once again the model performs well on the final three days of snow surveys, most
notably on Jan. 29/09, with RMSD values for those three days ranging from 0.010 m to 0.023 m
and NS values ranging from 0.977 to 0.995. The model still performs poorly on the first two
survey days but performs slightly better at the field scale then at the point scale. The amount of
overestimation and underestimation is within 15% at the field scale which is slightly closer to the
observations than the point scale modeling results over the last three days of snow surveys. The
model underestimates snow depth by 91% on the first survey day which is slightly better than the
point scale results but then over estimates by 63% on the second survey day which is worse than
the result at the point scale. The faults of the results are likely due to uncertainty in the modelling
of blowing snow over both complex terrain and varying vegetation.
75
5.3.3 Field Scale Model Results: Distributed
The final method compares field observations that were assigned to each of the HRUs with
simulated snow depths using a distributed modelling approach at the field scale for each of the
five days of snow survey. RMSD, NS, and MB were calculated for each HRU and can be seen
below in Table 5-5.
Date RMSD (m) NS MB
Field 1 Stream Field 2 Field 1 Stream Field 2 Field 1 Stream Field 2
Dec. 08/08 0.058 0.162 0.033 0.132 -0.039 0.218 -0.928 -0.973 -0.881 Jan. 15/09 0.036 0.027 0.042 0.848 0.968 0.736 0.387 0.170 0.511 Jan. 21/09 0.012 0.020 0.010 0.992 0.987 0.994 0.088 0.111 0.078 Jan. 29/09 0.032 0.011 0.022 0.965 0.997 0.981 -0.186 -0.051 -0.139 Feb. 04/09 0.048 0.067 0.040 0.926 0.929 0.941 -0.271 -0.258 -0.242
Table 5-5 Root Mean Squared Deviation (RMSD), Nash-Sutcliffe coefficient (NS), and Model Bias (MB) for the
comparison of field-scale simulated snow depth in a distributed approach and observed snow depth for each HRU on
each date of snow transect surveys during the 2008-2009 winter season.
There is a large variation in the values of RMSD and NS which range from 0.010 m to 0.162 m
and -0.039 to 0.997 respectively. Although the model still fails to adequately simulate snow
depth during the initial snow accumulation period, the distributed approach does a better job than
the lumped approach on the second day of snow surveying and continues to perform well
throughout the remainder of the season. By examining the model performance for each HRU on
each survey date we can see that the model does not perform well at all on Dec. 08/08. On Jan.
15/09 the model still has trouble simulating snow depth in both Field 1 and Field 2 but does well
simulating it in the Stream, only overestimating by 17%. By Jan. 21/09 the model is performing
very well in all three HRUs and is overestimating by less than 11%. The model begins to lose
performance by Jan. 29/09 but is still performing well, especially in the Stream. The model is
now underestimating snow depth by less than 19% but is still within the acceptable range as
mentioned above. By the final survey date, Feb. 04/09, the model continues to lose performance
76
and underestimates snow depth in all three HRUs. This underestimation ranges from 24-27%
which although is worse than the previous survey date, is still within the acceptable range of
model performance. On the whole, the model performs better for the two field HRUs during the
latter three days of surveying but performs better during the middle three days for the Stream
HRU. Examinations of MB values indicate that the model is able to generate mid to late season
snow depth values that are moderately close to the observations, keeping well within the
acceptable range of 30%.
5.4 Summary
Field and model results are examined in this chapter. Field results of both meteorological and in
situ snow surveys demonstrate that the 2008-2009 winter season was above average for
temperature, relative humidity, and snow depth but was below average for wind speed, resulting
in a shorter than average winter season with larger amounts of snow depth and less than average
redistribution of snow. A constant wind direction allows for a definitive and predictable pattern
of snow distribution across the entire field site. Examination of cumulative snowfall and snow
depth suggest that the field site acts predominantly as a blowing snow source throughout the
majority of the winter season with the exception of the stream HRU acting as a blowing snow
sink from the end of December to the middle of January.
The model appears to perform fairly well in both the lumped and distributed approaches once a
stable base layer of snow is established on the ground. Early seasonal snow accumulation is not
modelled well no matter what approach is taken at any scale. The model also begins to lose
performance at the tail end of the season, specifically in the distributed approach but is still
performing at an acceptable range. When comparing the point scale with the field scale in the
77
lumped approach, the model performs almost identically with only a few minor differences.
When comparing the lumped approach to the distributed approach the performance is similar but
is spatially more accurate in the distributed approach due to the spatial discretization of this
modelling approach. Reasons for the poor model performance and sources of error will be
discussed further on in the discussion section of this thesis.
78
Chapter 6.
Discussion and Conclusions
6.1 Evaluating Model Performance and Sources of Error
Even though the model represented the average snow depth fairly well for most of the winter
season, there are many sources of error that influenced the outcome of the model which
prevented a better outcome. The following section discusses the model performance and sources
of error that affected the outcome of the model results. Some of the topics include proper terrain
representation, poor early-season simulation, model limitations, and adjustments to
meteorological forcing data.
Terrain representation was a challenge with this model. The model platform used in this study
assumed a flat terrain and did not allow for the incorporation of a digital elevation map or any
changes to topography within the basin. The only exception was the ability to adjust the HRU
elevation. Upon initial testing however, this proved to be effective only when the change in
elevation was significant (>15m) and over a significantly larger area than the HRUs created in
this study. Therefore it was assumed that the field site was flat. In actuality however, the total
change in elevation was 9 m and the field site had several topographic features including hills,
the creek, and a sloping terrain on either side of the creek. In addition to the natural topography
of the field site, there were many objects (both man-made and natural) that added to the
difficulty in accurately modelling the terrain. These objects included the many farm buildings
located at the centre of the field, the elevated driveway, and all of the trees that bordered the
property, driveway, and buildings. All of these variations in terrain create changes in the
distribution of snow as it accumulates on the ground throughout the winter season. The hills are
important areas for erosion and deposition of blowing snow on both the windward and leeward
79
sides respectively. The sloped terrain helps to channel saltating and suspended snow to areas of
lower topography, namely the creekbed which in turn, was the largest sink of blowing snow
across the entire field site. The steep banks of the narrow creek allowed for deep drifts to
accumulate on either side and in some instances, completely fill the 1.5 m deep creekbed,
creating little snow bridges across several sections of the creek. The farm buildings provide a
significant amount of sheltering effect and a fair amount of drifting was observed in the lee of
these buildings. However, due to the proximity of the buildings to the creek, much of the drifting
was contained within the creek bed and did not progress significantly into the downwind field.
The elevated driveway produces a small amount of drifting on either side. The tall trees that
surround the buildings and run along portions of the elevated driveway are considered to be
within the sheltering effects of these man-made objects and therefore did not significantly alter
the drifting that occurred. The trees that are located along the perimeter of the property act as
wind barriers and allow for the accumulation of deep snow drifts around their bases. Air flow
through these trees is complex and difficult to model realistically. Previous studies have been
conducted to observe the relationship between trees and snow including the effects of shelterbelt
trees and shrubs (Sturges, 1983) and snow fences (Tabler, 1980a). The version of CRHM used in
this study does have a module that can incorporate the effect of canopy interception and wind
flow through trees but it was not incorporated because it involves a much greater amount of input
variables which was far outside the realm of this study. Furthermore, without the coupling of
this model to a 3-D windflow and terrain model such as the Mason and Sykes three-dimensional
extension of the Jackson and Hunt theory (MS3DJH) terrain wind-flow model (Walmsley et al.,
1986), correct terrain model representation is unobtainable, therefore leading to increased error.
80
Secondary to the topic of proper terrain modelling would be the inclusion of an updated working
GIS interface. The version used in this thesis was ArcGIS/ArcView 9.3 but the model was
configured to use ArcView version 3.1 and would not allow for more than one HRU shape file to
be uploaded at a time. Personal conversation with the model developer, Tom Brown, from the
University of Saskatchewan has determined that this is an area that needs to be updated and
improved upon.
The model does not simulate the early onset of snow and this can be attributed to a combination
of module assumptions from both PBSM and MSM and the inability to accurately model
physical processes at a fine scale in the natural environment. As was mentioned above, the early
winter season had several small snowfall and melt periods which are very difficult to accurately
model. The MSM module negates any effect of energy coming from the ground, from
precipitation, and internally from within the snow pack, thus altering the energy and mass
balance equations. In the early winter season the heat energy coming from the substrate and from
rain can significantly affect the overlying snowpack. Internal changes to the snowpack are
minimal due to the presence of such a small amount of snow on the ground unless significant
snowfall has occurred in various phases, resulting in a stratified snowpack. Nevertheless, MSM
is unable to simulate these small periods of melt during the early part of the winter season.
PBSM sequentially distributes any transported snow from areas of low snow holding capacity to
areas of higher snow holding capacity regardless of wind direction. Although this method works
in theory, it is not always the case in the natural environment. As well, snow transport within
PBSM only occurs once the first HRU has reached its snow holding capacity. This becomes an
issue in the beginning of the winter season in both the lumped and distributed approaches. In the
lumped approach, a snow depth amount of 5 cm is needed before any snow transportation can
81
occur. In the distributed approach an amount of 5 cm and 10 cm is necessary to accumulate in
Field 2 and Field 1 respectively before any snow is distributed to the Stream. In addition to the
minimum snow depth requirements, the sequence in which snow transport occurs between HRUs
does not represent the natural process very well. Since there is no method of accounting for wind
direction within the module, PBSM distributed snow based solely on snow-holding capacity. In
the case for Strawberry Creek snow distribution would follow in the format of Field 2 to Field 1
and then into the Stream. This is not the natural format of the field site (as seen in Figure 4-6).
As well, the prevailing wind direction actually comes from the west, resulting in a natural
sequence of snow distribution from Field 1 to Stream and then to Field 2. In addition to the
above mentioned sources of error, another significant factor is the inability to simulate accurate
amounts of snow depth in the initial HRU due to the fact that data from outside of the study
domain cannot be captured before it enters the study domain.
Once however, all (or the majority) of the snow-holding capacities have been reached, the model
performs really well at simulating the average snow depth across the entire field site, as seen in
the model results section. The snowpack becomes one homogenous layer and snow transport is
allowed to flow naturally between the HRUs. This is evident in the middle of the winter season.
The end of season snowmelt underestimation is primarily due to the previously mentioned
assumptions found within the MSM module. The HRU that is best represented throughout the
entire season is Field 2. This is due to the fact that is has the lowest snow-holding capacity (5cm)
and any blowing snow is placed into this HRU before moving onto the next. Although the
natural progression would see blowing snow come from Field 1 and the Stream HRUs, or from
outside the study domain, the model‟s ability to represent this HRU well is partially coincidental.
82
Accounting for precipitation events throughout the winter season can be a challenging
endeavour. Initially, precipitation in the form of rain would be collected using a tipping-bucket
rain gauge and snowfall would be a product of the difference in changes of accumulated snow
depth from the SR50a snow depth sensor. However, after consulting with the model developer,
we came to realize that the current version of the CRHM platform did not allow for separate
precipitation inputs from rain and snow at the same time. It is assumed that the model user would
be using a Geonor precipitation sensor and that the difference between rain and snow would be
determined within the model by applying a set temperature to which precipitation would either
be rain or snow. These parameters are known as „tmax_allrain and tmax_allsnow‟. Unfortunately
this realization did not arise until halfway through the winter season and resulted in all
precipitation data in the form of rain being neglected. This was unfortunate because the heat
energy from rain can be a significant source of melting, especially in Southern Ontario.
The adjustments made to account for snowfall precipitation were necessary as there was no other
accessible method to account for this form of precipitation throughout the winter season. The
daily snow depth values from the SR50a sensor overestimate a bit more than the values from the
Waterloo-Wellington airport but were chosen because they represent values from the actual field
site rather than from a location 10km away. The calculations necessary to acquire the
precipitation data (difference in accumulated snowfall) are simple and straight forward but they
are heavily reliant on the quality of data acquired by the snow depth sensor. Fortunately though,
the sensor had good signal quality (between 152 and 210) 89.9% of the time.
83
6.2 Future Considerations
If given the task of performing this study over again, a few changes would be made. In terms of
modelling, PBSM would be coupled with the Energy Balance Snowmelt Model (EBSM) (Gray
and Landine, 1987) as well as with a terrain wind-flow model such as MS3DJH (Walmsley et al.,
1986). These models have proven to be very effective in prairie-like conditions.
In terms of instrumentation, a Geonor precipitation gauge and a particle detector would be added
to the list of instrumentation and would significantly increase model simulation results because
snowfall rates, blowing snow events, and proper designation and inclusion of both forms of
precipitation can all be accounted for. As well, CRHM should be updated so that it could
accommodate the newest version of a GIS interface. This would allow for an enhanced
representation of terrain through a more user-friendly interface by simultaneously incorporating
multiple shape files for each HRU as well as digital terrain models. In doing so, the sheltering
effects of farm buildings and surrounding trees could be incorporated and a better representation
of blowing snow redistribution would be possible.
In terms of methodology, the sampling strategy would be kept the same but the inclusion of
several snowpits along each transect where values for SWE and density would be collected.
These values would help in the testing of the model.
Temporal analysis of the model performance indicates that the model does very well at
simulating the average snow depth across the entire season, regardless of the difficulty of
attaining reasonable simulations for the initial onset of snow. This suggests that if given the
correct seasonal data, the model may be used as a tool to compare seasonal averages for any
number of studies across a number of years.
84
6.3 Conclusions
This thesis was an attempt at modelling snow depth across an agricultural field in a small
subcatchment in Southern Ontario during the 2008-2009 winter season. It incorporated the
modules of the Prairie Blowing Snow Model (PBSM) and the Minimal Snowmelt Model (MSM)
within the Cold Regions Hydrological Model platform. Two different modelling approaches
(Lumped and Distributed) were compared at various scales (point scale and field scale) to a
series of in situ snow depth measurements, collected from snow surveys, which were completed
throughout the winter season using a semi-automated snow depth sensor. The model performs
well to simulate mid season snow depth averages in both the lumped and distributed approaches
but has a hard time dealing with the onset of snow as well as the smaller scale effects of
vegetation and terrain. There was very little change to model performance when upscaled from
the point scale to the field scale. From an experimental point of view, this demonstrates that there
are no scaling effects to be found at this size of domain.
This model is much better suited for large-scaled applications where these small-scale effects are
negligible. When available, it is also best to couple the model with a 3-D terrain model which
will increase the model‟s ability to accurately simulate the conditions across the entire study
domain (Fang and Pomeroy, 2009; Essery and Pomeroy, 2004). Modelling the natural
environment is extremely challenging and unless you are able to factor in all of the possible
variables as they change throughout the entire season at every possible scale there is no way of
reproducing 100% of the natural environment. The solution is to focus on the objective and
attempt to minimize the amount of error being produced. Design the experiment to suit the study
domain. The results posted in this thesis however, demonstrate that it is still possible to simulate
seasonal snow depth at a variety of scales with relative accuracy. The Prairie Blowing Snow
85
Model was designed for much larger study domains but this thesis proves that with a little
modification to the model and forcing data and if coupled with a snowmelt module, acceptable
results can be generated at a much smaller scale.
86
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94
Appendix 1
Parameter Definitions:
Basin Module
basin_area (km2) - basin area.
hru area (km2) - HRU area.
hru_lat (°) - latitude.
hru_elev (m) - altitude.
hru_GSL (°) - ground slope.
hru_ASL (°) - aspect.
basin_name – name given to the basin
hru_names – name given to the HRUs
run_ID - integer number.
Obs Module
basin_area (km2) - basin area.
hru area (km2) - HRU area.
hru_elev (m) - altitude.
obs_elev (m) - altitude.
lapse_rate (°C/100m) - lapse rate correction.
tmax_allrain (°C) - precipitation is all rain when the temperature is greater or equal to this
value.
tmax_allsnow (°C) - precipitation is all snow when the temperature is less or equal to this
value.
catchadjust () – 0 = for none 1 = Goodison
ppt_daily_distrib () – 0 = daily precip all in first interval, 1 = equally divided over the day
MSM_Org Module
a1 (s) - Albedo decay time constant for cold snow.
a2 (s) - Albedo decay time constant for melting snow.
amin () - Minimum albedo for aged snow.
amax () - Maximum albedo for fresh snow.
smin (mm) - Minimum snowfall to refresh snow albedo.
Z0snow (m) - snow roughness length.
Zref (m) - reference height.
basin_area (km2) - basin area.
hru area (km2) - HRU area.
hru_elev (m) - altitude.
PBSM Module
fetch (m) - fetch distance. (300-1000m)
Ht (m) - crop height.
95
distrib () - distribution fractions. Value for HRU 1 controls snow transport into the basin.
N_S (1/m2) - vegetation number density.
A_S (m) - stalk diameter or silhouette.
basin_area (km2) - basin area.
hru_area (km2) - hru_area.
inhibit_evap (flag) - an output parameter set true when the SWE is greater than zero. It is
used to inhibit evaporation from the evaporation modules.
inhibit_bs (flag) - an input inhibiting blowing snow when set equal to 1. Inhibited HRU
is still able to receive drift from other HRUs.
96
Appendix 2
Dec. 08/08
Jan. 15/09
Jan. 21/09
334
335
336
337
338
339
340
341
342
343
344
0
10
20
30
40
50
60
70
0.0
0
30
.46
62
.37
95
.89
12
8.3
6
15
7.5
1
18
2.7
7
21
3.4
2
23
9.6
9
26
5.4
7
29
1.8
1
31
9.3
4
34
9.1
2
37
9.7
0
41
3.5
8
43
8.4
9
46
6.4
2
49
1.1
8
52
0.1
5
55
3.5
1
58
3.4
7
61
5.1
8
64
3.3
4
67
2.7
0
69
9.7
3
72
3.6
2
74
9.6
3
77
4.7
2
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 1 - Dec. 08/08
334
335
336
337
338
339
340
341
342
343
344
345
0
5
10
15
20
25
30
35
40
45
0.00
26.2
3
56.8
6
87.9
6
119.
92
151.
37
171.
91
197.
34
229.
12
263.
27
296.
40
329.
10
361.
41
392.
64
422.
87
452.
97
484.
81
516.
80
547.
50
577.
82
610.
33
640.
77
673.
82
707.
76
739.
42
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 1 - Jan. 15/09
334
336
338
340
342
344
346
0
10
20
30
40
50
60
70
80
90
0.00
20.9
649
.06
77.5
110
5.27
132.
4915
9.17
173.
0419
7.68
226.
4225
5.46
285.
3731
3.74
342.
3737
1.27
401.
1443
2.37
463.
5649
1.80
520.
8055
1.65
584.
4861
3.58
641.
2967
0.47
700.
0372
9.18
757.
09
Elev
atio
n (m
)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 1 - Jan. 21/09
335
336
337
338
339
340
341
342
343
344
0
10
20
30
40
50
60
70
80
0.00
25
.09
50
.57
76
.86
101.
90
127.
77
153.
37
178.
50
204.
59
230.
80
249.
81
267.
02
290.
21
312.
52
335.
24
367.
92
392.
52
417.
56
441.
64
465.
51
489.
45
513.
08
537.
57
562.
08
586.
88
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 3 - Jan. 21/09
330
332
334
336
338
340
342
344
346
348
0
10
20
30
40
50
60
70
80
90
100
0.0
0
38
.14
73
.46
11
2.2
7
15
3.0
3
18
8.5
1
22
7.0
0
26
4.3
3
30
3.1
0
34
1.7
6
37
8.1
1
40
5.9
4
44
6.1
6
48
6.3
5
52
8.0
5
57
0.7
6
61
3.4
8
65
5.6
2
69
8.0
0
73
7.5
4
78
1.0
4
82
1.6
7
86
1.4
5
90
4.9
9
94
5.9
0
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 2 - Dec. 08/08
330
332
334
336
338
340
342
344
346
348
0
10
20
30
40
50
60
70
80
90
100
0.00
36.8
9
73.0
1
10
9.7
2
14
5.7
0
18
1.3
3
21
6.6
1
25
5.4
4
30
1.3
5
34
4.8
8
37
8.8
1
39
7.9
5
43
3.1
6
46
8.2
6
50
5.8
7
54
4.5
1
58
3.9
9
62
4.2
2
66
2.2
2
70
0.7
2
73
7.6
5
77
6.9
0
83
1.7
9
87
0.9
3
91
3.3
5
95
6.6
8
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 2 - Jan 15/09
332
334
336
338
340
342
344
346
348
0
10
20
30
40
50
60
70
0.00
38.2
6
75.5
3
118.
07
160.
13
202.
78
243.
27
284.
18
324.
90
365.
76
389.
44
424.
91
461.
90
498.
19
534.
85
572.
98
610.
13
645.
80
683.
66
721.
17
758.
99
810.
67
850.
36
886.
61
921.
61
958.
20
Elev
atio
n (m
)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 2 - Jan. 21/09
332
334
336
338
340
342
344
346
0
20
40
60
80
100
120
0.00
23.3
9
48.7
3
71.7
7
95.3
4
119.
70
132.
99
143.
10
165.
57
187.
83
211.
15
236.
33
260.
89
285.
12
310.
06
334.
29
357.
33
381.
04
406.
25
430.
67
454.
81
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 4 - Jan. 21/09
97
Jan. 29/09
340
341
342
343
344
345
346
347
348
0
10
20
30
40
50
60
70
80
90
100
0.0
0
8.3
7
17
.07
26
.54
35
.81
47
.69
56
.74
66
.85
76
.22
85
.29
95
.53
10
4.3
9
11
4.5
2
12
4.1
7
13
5.2
3
14
7.1
8
15
7.8
4
16
9.7
9
17
9.9
6
19
0.4
6
20
1.4
0
21
2.2
9
22
3.6
5
23
4.9
5
24
6.7
3
25
9.1
9
27
0.4
6
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Western Transect - Jan. 21/09
338
339
340
341
342
343
344
345
346
0
5
10
15
20
25
30
35
40
45
0.00
25.9
9
52.1
5
77.4
7
103.
20
128.
65
154.
16
176.
82
200.
44
224.
62
249.
76
275.
15
300.
42
326.
03
352.
70
380.
45
405.
43
431.
54
458.
65
484.
84
510.
67
536.
34
561.
87
590.
90
614.
46
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Northern Transect - Jan. 21/09
330
332
334
336
338
340
342
344
346
348
0
10
20
30
40
50
60
70
80
0.00
41.2
4
85.2
6
127.
77
170.
18
213.
39
249.
81
282.
78
320.
04
367.
92
408.
27
449.
71
489.
45
529.
37
570.
44
611.
38
652.
60
695.
16
737.
09
778.
17
818.
73
858.
98
899.
02
Ele
vati
on
n (m
)
Sno
wd
ep
th (c
m)
Distance (m)
Southern Transect - Jan. 21/09
336
337
338
339
340
341
342
343
344
345
346
347
0
20
40
60
80
100
120
140
0.00
34.1
0
65.5
2
98.1
8
131.
58
154.
54
173.
16
206.
35
239.
41
273.
86
307.
51
341.
72
375.
95
409.
67
443.
57
478.
76
513.
97
547.
34
584.
16
620.
03
654.
84
695.
91
728.
95
759.
91
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 1 - Jan. 29/09
337
338
339
340
341
342
343
344
345
0
10
20
30
40
50
60
70
80
90
0.0
0
17
.11
34
.24
51
.58
68
.69
86
.76
10
3.7
8
12
1.3
6
13
9.4
2
15
6.5
7
17
5.1
6
19
1.5
1
20
9.3
0
22
6.7
9
24
4.0
7
26
1.5
8
27
9.1
0
29
6.2
2
30
3.9
3
31
2.4
0
32
8.9
1
34
5.6
5
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Northwestern (Road) Transect - Jan. 21/09
342
342.5
343
343.5
344
344.5
345
345.5
346
346.5
0
10
20
30
40
50
60
70
80
90
100
0.00
16.9
6
32.9
9
49.5
4
66.7
8
83.8
0
101.
04
116.
98
134.
61
151.
40
168.
67
186.
63
204.
82
222.
32
239.
36
256.
35
273.
71
291.
21
308.
84
325.
96
342.
55
359.
61
376.
10
391.
47
407.
97
425.
52
442.
71
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Eastern Transect - Jan. 21/09
332
334
336
338
340
342
344
346
348
0
20
40
60
80
100
120
0.00
38.0
4
77.4
3
117.
75
161.
00
209.
05
252.
08
294.
94
338.
63
377.
85
400.
48
437.
29
474.
80
513.
11
555.
16
593.
42
633.
44
673.
16
716.
15
762.
80
804.
99
848.
16
885.
98
923.
00
960.
86
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 2 - Jan. 29/09
98
332
334
336
338
340
342
344
346
0
10
20
30
40
50
60
70
80
90
0.0
0
26
.38
56
.23
81
.77
10
6.1
9
13
0.5
6
14
3.3
6
16
9.2
6
19
3.3
6
21
9.9
2
24
4.1
3
26
7.8
3
29
4.3
3
31
9.2
3
34
6.2
0
36
9.3
0
39
3.9
0
41
8.4
0
44
3.1
7
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 3 - Jan. 29/09
342
343
344
345
346
347
348
349
0
20
40
60
80
100
120
0.00
16
.84
29
.56
43
.31
58
.16
74
.67
91
.12
108.
04
125.
98
143.
08
161.
56
178.
90
196.
11
213.
29
225.
60
240.
20
256.
30
271.
45
287.
31
307.
26
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Western Transect - Jan. 29/09
338
339
340
341
342
343
344
345
0
5
10
15
20
25
30
35
40
45
0.00
25.5
1
52.5
3
80.5
2
107.
61
133.
44
158.
84
183.
38
208.
97
234.
80
261.
10
288.
06
314.
55
340.
16
366.
58
392.
93
418.
15
445.
26
471.
94
496.
92
524.
34
550.
60
579.
81
605.
48
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Northern Transect - Jan. 29/09
330
332
334
336
338
340
342
344
346
348
0
10
20
30
40
50
60
0.00
46.0
7
90.9
3
134.
68
177.
20
221.
45
258.
15
295.
66
335.
54
377.
69
419.
10
457.
02
496.
84
536.
60
576.
45
618.
04
660.
07
702.
96
746.
43
788.
22
827.
84
866.
87
907.
32
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Southern Transect - Jan. 29/09
336
337
338
339
340
341
342
343
344
345
0
20
40
60
80
100
120
0.0
0
26
.34
51
.87
77
.84
10
2.7
8
12
6.8
5
14
4.3
3
16
8.8
4
19
1.1
7
21
3.1
9
23
8.1
6
25
8.8
8
28
0.0
1
29
9.9
2
32
2.2
0
34
5.1
9
36
6.3
8
38
5.4
6
40
7.3
4
42
9.4
4
45
1.3
8
47
3.7
4
49
8.7
3
52
2.5
0
54
4.7
6
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 4 - Jan. 29/09
336
337
338
339
340
341
342
343
344
345
0
10
20
30
40
50
60
70
80
0.00
16.7
4
33.0
3
50.6
8
66.9
2
83.7
4
99.5
6
115.
10
132.
67
149.
07
166.
25
184.
83
200.
88
217.
43
233.
95
249.
44
264.
46
281.
39
298.
05
308.
11
322.
63
338.
14
354.
17
Ele
vati
on
(m)
Sno
wd
epth
(cm
)
Distance (m)
Northwestern (Road) Transect - Jan. 29/09
341
342
343
344
345
346
347
0
10
20
30
40
50
60
70
80
0.00
23.9
8
46.6
1
70.2
6
92.7
4
115.
60
136.
81
158.
76
181.
96
205.
34
229.
36
252.
06
274.
83
298.
97
324.
78
350.
34
372.
90
396.
14
421.
76
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Eastern Transect - Jan. 29/09
99
Feb. 04/09
335
336
337
338
339
340
341
342
343
344
345
0
20
40
60
80
100
120
0.0
0
33
.36
67
.17
10
0.7
3
13
3.4
9
15
1.1
5
18
5.4
0
22
1.1
1
25
6.3
3
29
1.1
1
32
6.0
8
36
0.0
4
39
4.9
8
43
0.9
4
46
7.2
5
50
0.5
8
53
3.9
2
57
1.7
0
60
6.7
9
64
1.8
5
67
6.5
4
71
2.2
4
74
4.9
2
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 1 - Feb. 04/09
332
334
336
338
340
342
344
0
10
20
30
40
50
60
70
80
90
100
0.00
16.7
2
33.6
3
54.1
7
71.2
4
87.9
4
103.
83
119.
18
129.
19
141.
39
157.
49
172.
79
190.
78
208.
54
226.
04
243.
89
261.
91
281.
06
299.
65
317.
83
335.
01
352.
33
370.
07
387.
17
404.
79
422.
90
439.
97
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 3 - Feb. 04/09
340
341
342
343
344
345
346
347
0
10
20
30
40
50
60
70
80
90
100
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Western Transect - Feb. 04/09
337
338
339
340
341
342
343
344
0
5
10
15
20
25
30
35
40
45
50
0.00
28
.15
54
.47
81
.34
108.
71
136.
47
162.
89
189.
82
216.
63
244.
14
270.
19
296.
07
320.
51
347.
56
373.
79
399.
20
426.
26
453.
91
480.
28
507.
90
535.
12
562.
55
589.
11
615.
60
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Northern Transect - Feb. 04/09
330
332
334
336
338
340
342
344
346
0
20
40
60
80
100
120
140
0.0
0
38
.51
78
.11
12
0.5
9
16
7.0
9
21
8.1
2
26
7.5
6
31
1.5
4
35
7.6
6
39
0.0
2
42
3.2
1
46
2.6
7
50
3.9
2
54
6.1
8
58
9.0
9
62
8.7
7
67
0.1
3
71
4.9
9
75
9.2
9
80
5.8
5
86
5.3
9
90
7.7
7
94
8.9
9
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Transect 2 - Feb. 04/09
335
336
337
338
339
340
341
342
343
344
0
10
20
30
40
50
60
70
80
90
0.00
25.6
6
51.6
6
78.5
2
105.…
132.…
147.…
171.…
198.…
223.…
248.…
272.…
298.…
324.…
351.…
374.…
404.…
429.…
454.…
480.…
507.…
532.…
557.…
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Transect 4 - Feb. 04/09
334
335
336
337
338
339
340
341
342
343
344
345
0
10
20
30
40
50
60
70
80
90
100
0.00
16.6
8
32.7
7
48.7
0
66.6
1
83.8
3
100.
63
117.
26
135.
05
152.
01
172.
46
188.
36
205.
75
221.
71
239.
58
256.
78
271.
86
288.
15
302.
07
312.
98
330.
52
346.
68
Ele
vati
on
(m)
Sno
wd
ep
th (c
m)
Distance (m)
Northwestern (Road) Transect - Feb. 04/09
339.5
340
340.5
341
341.5
342
342.5
343
343.5
344
344.5
0
10
20
30
40
50
60
70
80
0.00
21.7
2
41.4
9
65.0
5
94.1
1
119.
94
145.
14
170.
48
195.
77
220.
25
244.
00
266.
68
287.
96
309.
01
331.
58
356.
26
382.
78
408.
42
434.
80
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Eastern Transect - Feb. 04/09
100
328
330
332
334
336
338
340
342
344
346
0
10
20
30
40
50
60
70
80
90
0.0
0
35
.63
71
.01
10
5.5
5
13
8.9
8
17
3.6
9
21
4.8
3
25
0.5
2
28
3.7
6
31
3.0
8
34
5.3
3
38
0.1
6
41
3.0
1
44
7.6
9
48
2.8
0
51
9.2
8
55
3.3
9
59
0.0
4
62
6.7
4
66
2.7
4
69
9.8
2
73
5.0
3
77
3.7
5
81
3.9
8
85
5.3
4
89
1.1
1
92
4.8
7
Elev
atio
n (m
)
Sno
wd
epth
(cm
)
Distance (m)
Southern Transect - Feb. 04/09
